LMFDB - Embedded newform 392.3.k.j.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.796594176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 83x^4 - 104x^3 + 22x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$-0.207107 + 2.54762i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.j.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +O(q^{10})$	\(q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +(2.39883 + 1.96308i) q^{10} +(2.24264 + 3.88437i) q^{11} +(2.70163 + 13.3870i) q^{12} -1.54985i q^{13} -5.29150i q^{15} +(12.7477 + 9.66930i) q^{16} +(11.8284 + 20.4874i) q^{17} +(3.36526 - 4.11224i) q^{18} +(-12.4350 + 21.5381i) q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(30.5055 + 17.6124i) q^{23} +(-1.00775 - 27.2951i) q^{24} +(-11.2990 - 19.5704i) q^{25} +(-0.500665 + 3.05899i) q^{26} +21.6569 q^{27} +22.4499i q^{29} +(-1.70938 + 10.4440i) q^{30} +(-40.4569 + 23.3578i) q^{31} +(-22.0371 - 23.2027i) q^{32} +(-7.65685 + 13.2621i) q^{33} +(-16.7279 - 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(-50.7340 - 29.2913i) q^{37} +(31.5012 - 38.4935i) q^{38} +(4.58258 - 2.64575i) q^{39} +(6.59133 + 10.5016i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(3.54915 + 17.5866i) q^{44} +(3.56604 - 2.05886i) q^{45} +(-54.5204 - 44.6168i) q^{46} +(31.2918 + 18.0663i) q^{47} +(-6.82843 + 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 + 69.9485i) q^{51} +(1.97636 - 5.87591i) q^{52} +(-84.7102 + 48.9075i) q^{53} +(-42.7450 - 6.99607i) q^{54} -6.95149i q^{55} -84.9117 q^{57} +(7.25227 - 44.3103i) q^{58} +(30.7782 + 53.3094i) q^{59} +(6.74773 - 20.0616i) q^{60} +(32.6340 + 18.8412i) q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 + 2.08021i) q^{65} +(19.3968 - 23.7024i) q^{66} +(16.6863 + 28.9015i) q^{67} +(18.7194 + 92.7574i) q^{68} +120.265i q^{69} -102.199i q^{71} +(18.0026 - 11.2993i) q^{72} +(34.6569 + 60.0274i) q^{73} +(90.6733 + 74.2026i) q^{74} +(38.5772 - 66.8176i) q^{75} +(-74.6102 + 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(33.5156 + 19.3503i) q^{79} +(-9.61710 - 22.8567i) q^{80} +(48.9264 + 84.7430i) q^{81} +(-53.2328 - 8.71262i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(33.8922 + 5.54714i) q^{86} +(-66.3799 + 38.3245i) q^{87} +(-1.32389 - 35.8578i) q^{88} +(22.0294 - 38.1561i) q^{89} +(-7.70354 + 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(-138.129 - 79.7486i) q^{93} +(-55.9256 - 45.7668i) q^{94} +(33.3807 - 19.2724i) q^{95} +(30.9861 - 104.769i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9	$ 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9} - 28 q^{10} - 16 q^{11} - 24 q^{12} - 8 q^{16} + 72 q^{17} - 16 q^{18} + 8 q^{19} - 112 q^{20} - 48 q^{22} - 40 q^{24} + 68 q^{25} + 28 q^{26} + 128 q^{27} - 16 q^{33} - 32 q^{34} + 72 q^{36} - 76 q^{38} + 56 q^{40} + 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} - 32 q^{48} + 224 q^{50} - 176 q^{51} - 56 q^{52} - 16 q^{54} - 272 q^{57} + 168 q^{58} + 184 q^{59} - 56 q^{60} + 224 q^{62} + 288 q^{64} - 168 q^{65} - 32 q^{66} + 224 q^{67} - 216 q^{68} + 160 q^{72} + 232 q^{73} + 280 q^{74} + 88 q^{75} + 48 q^{76} - 336 q^{80} + 52 q^{81} - 48 q^{82} - 176 q^{83} - 8 q^{86} - 240 q^{88} + 312 q^{89} - 616 q^{90} + 112 q^{92} - 112 q^{94} + 176 q^{96} + 272 q^{97} - 480 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9 - 28 * q^10 - 16 * q^11 - 24 * q^12 - 8 * q^16 + 72 * q^17 - 16 * q^18 + 8 * q^19 - 112 * q^20 - 48 * q^22 - 40 * q^24 + 68 * q^25 + 28 * q^26 + 128 * q^27 - 16 * q^33 - 32 * q^34 + 72 * q^36 - 76 * q^38 + 56 * q^40 + 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 - 32 * q^48 + 224 * q^50 - 176 * q^51 - 56 * q^52 - 16 * q^54 - 272 * q^57 + 168 * q^58 + 184 * q^59 - 56 * q^60 + 224 * q^62 + 288 * q^64 - 168 * q^65 - 32 * q^66 + 224 * q^67 - 216 * q^68 + 160 * q^72 + 232 * q^73 + 280 * q^74 + 88 * q^75 + 48 * q^76 - 336 * q^80 + 52 * q^81 - 48 * q^82 - 176 * q^83 - 8 * q^86 - 240 * q^88 + 312 * q^89 - 616 * q^90 + 112 * q^92 - 112 * q^94 + 176 * q^96 + 272 * q^97 - 480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.97374	−	0.323042i	−0.986869	−	0.161521i
$2$	−1.97374	−	0.323042i	−0.986869	−	0.161521i
$3$	1.70711	+	2.95680i	0.569036	+	0.985599i	0.996662	+	0.0816428i	$0.0260167\pi$
$3$	1.70711	+	2.95680i	0.569036	+	0.985599i	−0.427626	+	0.903956i	$0.640650\pi$
$4$	3.79129	+	1.27520i	0.947822	+	0.318800i
$5$	−1.34221	−	0.774923i	−0.268441	−	0.154985i	0.359738	−	0.933053i	$-0.382866\pi$
$5$	−1.34221	−	0.774923i	−0.268441	−	0.154985i	−0.628179	+	0.778069i	$0.716199\pi$
$6$	−2.41421	−	6.38741i	−0.402369	−	1.06457i
$7$		0			0
$7$		0			0
$8$	−7.07107	−	3.74166i	−0.883883	−	0.467707i
$9$	−1.32843	+	2.30090i	−0.147603	+	0.255656i
$10$	2.39883	+	1.96308i	0.239883	+	0.196308i
$11$	2.24264	+	3.88437i	0.203876	+	0.353124i	0.949774	−	0.312936i	$-0.101313\pi$
$11$	2.24264	+	3.88437i	0.203876	+	0.353124i	−0.745898	+	0.666060i	$0.767979\pi$
$12$	2.70163	+	13.3870i	0.225135	+	1.11558i
$13$		−	1.54985i		−	0.119219i	−0.998222	−	0.0596094i	$-0.981014\pi$
$13$		−	1.54985i		−	0.119219i	0.998222	−	0.0596094i	$-0.0189855\pi$
$14$		0			0
$15$		−	5.29150i		−	0.352767i
$16$	12.7477	+	9.66930i	0.796733	+	0.604332i
$17$	11.8284	+	20.4874i	0.695790	+	1.20514i	0.969914	+	0.243449i	$0.0782788\pi$
$17$	11.8284	+	20.4874i	0.695790	+	1.20514i	−0.274124	+	0.961694i	$0.588388\pi$
$18$	3.36526	−	4.11224i	0.186959	−	0.228458i
$19$	−12.4350	+	21.5381i	−0.654475	+	1.13358i	0.327550	+	0.944834i	$0.393777\pi$
$19$	−12.4350	+	21.5381i	−0.654475	+	1.13358i	−0.982025	+	0.188750i	$0.939556\pi$
$20$	−4.10051	−	4.64954i	−0.205025	−	0.232477i
$21$		0			0
$22$	−3.17157	−	8.39119i	−0.144162	−	0.381418i
$23$	30.5055	+	17.6124i	1.32633	+	0.765756i	0.984730	−	0.174090i	$-0.0556985\pi$
$23$	30.5055	+	17.6124i	1.32633	+	0.765756i	0.341598	+	0.939846i	$0.389032\pi$
$24$	−1.00775	−	27.2951i	−0.0419896	−	1.13730i
$25$	−11.2990	−	19.5704i	−0.451960	−	0.782817i
$26$	−0.500665	+	3.05899i	−0.0192563	+	0.117653i
$27$	21.6569			0.802106
$28$		0			0
$29$			22.4499i			0.774136i	0.922051	+	0.387068i	$0.126512\pi$
$29$			22.4499i			0.774136i	−0.922051	+	0.387068i	$0.873488\pi$
$30$	−1.70938	+	10.4440i	−0.0569792	+	0.348135i
$31$	−40.4569	+	23.3578i	−1.30506	+	0.753478i	−0.981268	−	0.192649i	$-0.938292\pi$
$31$	−40.4569	+	23.3578i	−1.30506	+	0.753478i	−0.323795	+	0.946127i	$0.604959\pi$
$32$	−22.0371	−	23.2027i	−0.688659	−	0.725085i
$33$	−7.65685	+	13.2621i	−0.232026	+	0.401881i
$34$	−16.7279	−	44.2579i	−0.491998	−	1.30170i
$35$		0			0
$36$	−7.97056	+	7.02938i	−0.221405	+	0.195260i
$37$	−50.7340	−	29.2913i	−1.37119	−	0.791657i	−0.380111	−	0.924941i	$-0.624114\pi$
$37$	−50.7340	−	29.2913i	−1.37119	−	0.791657i	−0.991078	+	0.133284i	$0.957448\pi$
$38$	31.5012	−	38.4935i	0.828979	−	1.01299i
$39$	4.58258	−	2.64575i	0.117502	−	0.0678398i
$40$	6.59133	+	10.5016i	0.164783	+	0.262540i
$41$	26.9706			0.657819			0.328909	−	0.944362i	$-0.393319\pi$
$41$	26.9706			0.657819			0.328909	+	0.944362i	$0.393319\pi$
$42$		0			0
$43$	−17.1716			−0.399339			−0.199669	−	0.979863i	$-0.563987\pi$
$43$	−17.1716			−0.399339			−0.199669	+	0.979863i	$0.563987\pi$
$44$	3.54915	+	17.5866i	0.0806625	+	0.399695i
$45$	3.56604	−	2.05886i	0.0792454	−	0.0457524i
$46$	−54.5204	−	44.6168i	−1.18523	−	0.969930i
$47$	31.2918	+	18.0663i	0.665783	+	0.384390i	0.794477	−	0.607295i	$-0.207745\pi$
$47$	31.2918	+	18.0663i	0.665783	+	0.384390i	−0.128694	+	0.991684i	$0.541079\pi$
$48$	−6.82843	+	54.1990i	−0.142259	+	1.12915i
$49$		0			0
$50$	15.9792	+	42.2769i	0.319584	+	0.845539i
$51$	−40.3848	+	69.9485i	−0.791858	+	1.37154i
$52$	1.97636	−	5.87591i	0.0380070	−	0.112998i
$53$	−84.7102	+	48.9075i	−1.59831	+	0.922782i	−0.606492	+	0.795090i	$0.707424\pi$
$53$	−84.7102	+	48.9075i	−1.59831	+	0.922782i	−0.991814	+	0.127693i	$0.959243\pi$
$54$	−42.7450	−	6.99607i	−0.791573	−	0.129557i
$55$		−	6.95149i		−	0.126391i
$56$		0			0
$57$	−84.9117			−1.48968
$58$	7.25227	−	44.3103i	0.125039	−	0.763971i
$59$	30.7782	+	53.3094i	0.521664	+	0.903549i	0.999682	+	0.0251987i	$0.00802186\pi$
$59$	30.7782	+	53.3094i	0.521664	+	0.903549i	−0.478018	+	0.878350i	$0.658645\pi$
$60$	6.74773	−	20.0616i	0.112462	−	0.334360i
$61$	32.6340	+	18.8412i	0.534983	+	0.308873i	0.743043	−	0.669243i	$-0.233382\pi$
$61$	32.6340	+	18.8412i	0.534983	+	0.308873i	−0.208060	+	0.978116i	$0.566715\pi$
$62$	87.3970	−	33.0329i	1.40963	−	0.532790i
$63$		0			0
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$	−1.20101	+	2.08021i	−0.0184771	+	0.0320032i
$66$	19.3968	−	23.7024i	0.293891	−	0.359127i
$67$	16.6863	+	28.9015i	0.249049	+	0.431366i	0.963262	−	0.268563i	$-0.0865486\pi$
$67$	16.6863	+	28.9015i	0.249049	+	0.431366i	−0.714213	+	0.699928i	$0.753215\pi$
$68$	18.7194	+	92.7574i	0.275285	+	1.36408i
$69$			120.265i			1.74297i
$70$		0			0
$71$		−	102.199i		−	1.43942i	−0.694277	−	0.719708i	$-0.744276\pi$
$71$		−	102.199i		−	1.43942i	0.694277	−	0.719708i	$-0.255724\pi$
$72$	18.0026	−	11.2993i	0.250036	−	0.156935i
$73$	34.6569	+	60.0274i	0.474751	+	0.822294i	0.999582	−	0.0289132i	$-0.00920463\pi$
$73$	34.6569	+	60.0274i	0.474751	+	0.822294i	−0.524830	+	0.851207i	$0.675871\pi$
$74$	90.6733	+	74.2026i	1.22532	+	1.00274i
$75$	38.5772	−	66.8176i	0.514362	−	0.890901i
$76$	−74.6102	+	65.8000i	−0.981713	+	0.865789i
$77$		0			0
$78$	−9.89949	+	3.74166i	−0.126917	+	0.0479700i
$79$	33.5156	+	19.3503i	0.424248	+	0.244940i	0.696893	−	0.717175i	$-0.254565\pi$
$79$	33.5156	+	19.3503i	0.424248	+	0.244940i	−0.272645	+	0.962115i	$0.587898\pi$
$80$	−9.61710	−	22.8567i	−0.120214	−	0.285709i
$81$	48.9264	+	84.7430i	0.604030	+	1.04621i
$82$	−53.2328	−	8.71262i	−0.649181	−	0.106251i
$83$	−3.61522			−0.0435569			−0.0217785	−	0.999763i	$-0.506933\pi$
$83$	−3.61522			−0.0435569			−0.0217785	+	0.999763i	$0.506933\pi$
$84$		0			0
$85$		−	36.6645i		−	0.431347i
$86$	33.8922	+	5.54714i	0.394095	+	0.0645016i
$87$	−66.3799	+	38.3245i	−0.762987	+	0.440511i
$88$	−1.32389	−	35.8578i	−0.0150442	−	0.407475i
$89$	22.0294	−	38.1561i	0.247522	−	0.428720i	−0.715316	−	0.698801i	$-0.753717\pi$
$89$	22.0294	−	38.1561i	0.247522	−	0.428720i	0.962838	+	0.270081i	$0.0870505\pi$
$90$	−7.70354	+	2.91166i	−0.0855948	+	0.0323518i
$91$		0			0
$92$	93.1960	+	105.674i	1.01300	+	1.14863i
$93$	−138.129	−	79.7486i	−1.48525	−	0.857512i
$94$	−55.9256	−	45.7668i	−0.594953	−	0.486880i
$95$	33.3807	−	19.2724i	0.351376	−	0.202867i
$96$	30.9861	−	104.769i	0.322772	−	1.09134i
$97$	−96.1076			−0.990800			−0.495400	−	0.868665i	$-0.664979\pi$
$97$	−96.1076			−0.990800			−0.495400	+	0.868665i	$0.664979\pi$
$98$		0			0
$99$	−11.9167			−0.120371
$100$	−17.8815	−	88.6056i	−0.178815	−	0.886056i
$101$	16.9881	−	9.80808i	0.168199	−	0.0971097i	−0.413537	−	0.910487i	$-0.635707\pi$
$101$	16.9881	−	9.80808i	0.168199	−	0.0971097i	0.581736	+	0.813377i	$0.302374\pi$
$102$	102.305	−	125.014i	1.00299	−	1.22563i
$103$	−37.3120	−	21.5421i	−0.362252	−	0.209146i	0.307816	−	0.951446i	$-0.400402\pi$
$103$	−37.3120	−	21.5421i	−0.362252	−	0.209146i	−0.670068	+	0.742300i	$0.733735\pi$
$104$	−5.79899	+	10.9591i	−0.0557595	+	0.105376i
$105$		0			0
$106$	182.995	−	69.1656i	1.72637	−	0.652506i
$107$	−7.79899	+	13.5082i	−0.0728878	+	0.126245i	−0.900166	−	0.435547i	$-0.856555\pi$
$107$	−7.79899	+	13.5082i	−0.0728878	+	0.126245i	0.827278	+	0.561793i	$0.189888\pi$
$108$	82.1074	+	27.6168i	0.760253	+	0.255711i
$109$	−3.33576	+	1.92590i	−0.0306033	+	0.0176688i	−0.515224	−	0.857056i	$-0.672291\pi$
$109$	−3.33576	+	1.92590i	−0.0306033	+	0.0176688i	0.484620	+	0.874725i	$0.338958\pi$
$110$	−2.24562	+	13.7204i	−0.0204148	+	0.124731i
$111$		−	200.013i		−	1.80192i
$112$		0			0
$113$	−13.7746			−0.121899			−0.0609496	−	0.998141i	$-0.519413\pi$
$113$	−13.7746			−0.121899			−0.0609496	+	0.998141i	$0.519413\pi$
$114$	167.593	+	27.4300i	1.47012	+	0.240614i
$115$	−27.2965	−	47.2789i	−0.237361	−	0.411121i
$116$	−28.6282	+	85.1142i	−0.246795	+	0.733743i
$117$	3.56604	+	2.05886i	0.0304790	+	0.0175971i
$118$	−43.5269	−	115.161i	−0.368872	−	0.975944i
$119$		0			0
$120$	−19.7990	+	37.4166i	−0.164992	+	0.311805i
$121$	50.4411	−	87.3666i	0.416869	−	0.722038i
$122$	−58.3245	−	47.7298i	−0.478069	−	0.391228i
$123$	46.0416	+	79.7464i	0.374322	+	0.648345i
$124$	−183.170	+	36.9655i	−1.47718	+	0.298109i
$125$			73.7695i			0.590156i
$126$		0			0
$127$		−	125.025i		−	0.984445i	−0.870469	−	0.492223i	$-0.836185\pi$
$127$		−	125.025i		−	0.984445i	0.870469	−	0.492223i	$-0.163815\pi$
$128$	−53.9608	−	116.070i	−0.421569	−	0.906796i
$129$	−29.3137	−	50.7728i	−0.227238	−	0.393588i
$130$	3.04248	−	3.71782i	0.0234037	−	0.0285986i
$131$	50.1751	−	86.9059i	0.383016	−	0.663404i	−0.608475	−	0.793573i	$-0.708219\pi$
$131$	50.1751	−	86.9059i	0.383016	−	0.663404i	0.991492	+	0.130169i	$0.0415519\pi$
$132$	−45.9411	+	40.5163i	−0.348039	+	0.306941i
$133$		0			0
$134$	−23.5980	−	62.4344i	−0.176104	−	0.465928i
$135$	−29.0679	−	16.7824i	−0.215318	−	0.124314i
$136$	−6.98264	−	189.126i	−0.0513430	−	1.39063i
$137$	−28.6569	−	49.6351i	−0.209174	−	0.362300i	0.742280	−	0.670089i	$-0.233744\pi$
$137$	−28.6569	−	49.6351i	−0.209174	−	0.362300i	−0.951455	+	0.307789i	$0.900411\pi$
$138$	38.8506	−	237.371i	0.281526	−	1.72008i
$139$	183.664			1.32132			0.660662	−	0.750684i	$-0.270276\pi$
$139$	183.664			1.32132			0.660662	+	0.750684i	$0.270276\pi$
$140$		0			0
$141$			123.365i			0.874926i
$142$	−33.0144	+	201.713i	−0.232496	+	1.42052i
$143$	6.02017	−	3.47575i	0.0420991	−	0.0243059i
$144$	−39.1826	+	16.4863i	−0.272101	+	0.114488i
$145$	17.3970	−	30.1324i	0.119979	−	0.207810i
$146$	−49.0122	−	129.674i	−0.335700	−	0.888179i
$147$		0			0
$148$	−154.995	−	175.748i	−1.04726	−	1.18748i
$149$	166.545	+	96.1549i	1.11775	+	0.645335i	0.940826	−	0.338889i	$-0.110051\pi$
$149$	166.545	+	96.1549i	1.11775	+	0.645335i	0.176927	+	0.984224i	$0.443384\pi$
$150$	−97.7261	+	119.418i	−0.651508	+	0.796123i
$151$	99.3791	−	57.3765i	0.658140	−	0.379977i	−0.133428	−	0.991058i	$-0.542599\pi$
$151$	99.3791	−	57.3765i	0.658140	−	0.379977i	0.791568	+	0.611081i	$0.209265\pi$
$152$	168.517	−	105.770i	1.10867	−	0.695854i
$153$	−62.8528			−0.410803
$154$		0			0
$155$	72.4020			0.467110
$156$	20.7477	−	4.18710i	0.132998	−	0.0268404i
$157$	−183.724	+	106.073i	−1.17022	+	0.675625i	−0.953731	−	0.300661i	$-0.902793\pi$
$157$	−183.724	+	106.073i	−1.17022	+	0.675625i	−0.216486	+	0.976286i	$0.569460\pi$
$158$	−59.9001	−	49.0193i	−0.379115	−	0.310249i
$159$	−289.219	−	166.981i	−1.81899	−	1.05019i
$160$	11.5980	+	48.2199i	0.0724874	+	0.301374i
$161$		0			0
$162$	−69.1924	−	183.066i	−0.427114	−	1.13004i
$163$	120.267	−	208.309i	0.737835	−	1.27797i	−0.215634	−	0.976474i	$-0.569182\pi$
$163$	120.267	−	208.309i	0.737835	−	1.27797i	0.953469	−	0.301493i	$-0.0974849\pi$
$164$	102.253	+	34.3929i	0.623495	+	0.209713i
$165$	20.5541	−	11.8669i	0.124571	−	0.0719208i
$166$	7.13551	+	1.16787i	0.0429850	+	0.00703535i
$167$		−	212.101i		−	1.27006i	−0.772486	−	0.635032i	$-0.780987\pi$
$167$		−	212.101i		−	1.27006i	0.772486	−	0.635032i	$-0.219013\pi$
$168$		0			0
$169$	166.598			0.985787
$170$	−11.8442	+	72.3661i	−0.0696715	+	0.425683i
$171$	−33.0381	−	57.2236i	−0.193205	−	0.334641i
$172$	−65.1024	−	21.8972i	−0.378502	−	0.127309i
$173$	157.801	+	91.1065i	0.912145	+	0.526627i	0.881121	−	0.472891i	$-0.156790\pi$
$173$	157.801	+	91.1065i	0.912145	+	0.526627i	0.0310245	+	0.999519i	$0.490123\pi$
$174$	143.397	−	54.1990i	0.824121	−	0.311488i
$175$		0			0
$176$	−8.97056	+	71.2016i	−0.0509691	+	0.404555i
$177$	−105.083	+	182.010i	−0.593691	+	1.02830i
$178$	−55.8064	+	68.1937i	−0.313519	+	0.383111i
$179$	−28.6030	−	49.5419i	−0.159793	−	0.276770i	0.775001	−	0.631960i	$-0.217749\pi$
$179$	−28.6030	−	49.5419i	−0.159793	−	0.276770i	−0.934794	+	0.355190i	$0.884416\pi$
$180$	16.1454	−	3.25830i	0.0896964	−	0.0181016i
$181$			326.212i			1.80228i	0.433533	+	0.901138i	$0.357267\pi$
$181$			326.212i			1.80228i	−0.433533	+	0.901138i	$0.642733\pi$
$182$		0			0
$183$			128.656i			0.703039i
$184$	−149.807	−	238.680i	−0.814170	−	1.29717i
$185$	45.3970	+	78.6299i	0.245389	+	0.425026i
$186$	246.868	+	202.024i	1.32725	+	1.08615i
$187$	−53.0538	+	91.8919i	−0.283710	+	0.491401i
$188$	95.5980	+	108.398i	0.508500	+	0.576585i
$189$		0			0
$190$	−72.1106	+	27.2552i	−0.379530	+	0.143449i
$191$	84.0589	+	48.5314i	0.440099	+	0.254091i	0.703639	−	0.710557i	$-0.251557\pi$
$191$	84.0589	+	48.5314i	0.440099	+	0.254091i	−0.263541	+	0.964648i	$0.584890\pi$
$192$	−95.0031	+	196.776i	−0.494808	+	1.02488i
$193$	−78.6518	−	136.229i	−0.407522	−	0.705849i	0.587089	−	0.809522i	$-0.300274\pi$
$193$	−78.6518	−	136.229i	−0.407522	−	0.705849i	−0.994611	+	0.103673i	$0.966940\pi$
$194$	189.691	+	31.0468i	0.977791	+	0.160035i
$195$	−8.20101			−0.0420565
$196$		0			0
$197$			124.117i			0.630034i	0.949086	+	0.315017i	$0.102010\pi$
$197$			124.117i			0.630034i	−0.949086	+	0.315017i	$0.897990\pi$
$198$	23.5205	+	3.84961i	0.118791	+	0.0194425i
$199$	156.729	−	90.4874i	0.787581	−	0.454710i	−0.0515289	−	0.998672i	$-0.516409\pi$
$199$	156.729	−	90.4874i	0.787581	−	0.454710i	0.839110	+	0.543961i	$0.183076\pi$
$200$	6.67010	+	180.661i	0.0333505	+	0.903304i
$201$	−56.9706	+	98.6759i	−0.283436	+	0.490925i
$202$	−36.6985	+	13.8707i	−0.181676	+	0.0686669i
$203$		0			0
$204$	−242.309	+	213.696i	−1.18779	+	1.04753i
$205$	−36.2000	−	20.9001i	−0.176586	−	0.101952i
$206$	66.6851	+	54.5717i	0.323714	+	0.264911i
$207$	−81.0488	+	46.7935i	−0.391540	+	0.226056i
$208$	14.9859	−	19.7570i	0.0720477	−	0.0949856i
$209$	−111.549			−0.533728
$210$		0			0
$211$	164.049			0.777482			0.388741	−	0.921347i	$-0.372910\pi$
$211$	164.049			0.777482			0.388741	+	0.921347i	$0.372910\pi$
$212$	−383.528	+	77.3998i	−1.80909	+	0.365093i
$213$	302.180	−	174.464i	1.41869	−	0.819079i
$214$	19.7569	−	24.1423i	0.0923219	−	0.112815i
$215$	23.0478	+	13.3066i	0.107199	+	0.0618913i
$216$	−153.137	−	81.0325i	−0.708968	−	0.375151i
$217$		0			0
$218$	7.20606	−	2.72363i	0.0330553	−	0.0124937i
$219$	−118.326	+	204.946i	−0.540301	+	0.935829i
$220$	8.86455	−	26.3551i	0.0402934	−	0.119796i
$221$	31.7524	−	18.3322i	0.143676	−	0.0829513i
$222$	−64.6127	+	394.774i	−0.291048	+	1.77826i
$223$			10.5830i			0.0474574i	0.999718	+	0.0237287i	$0.00755379\pi$
$223$			10.5830i			0.0474574i	−0.999718	+	0.0237287i	$0.992446\pi$
$224$		0			0
$225$	60.0395			0.266842
$226$	27.1875	+	4.44977i	0.120299	+	0.0196893i
$227$	52.9031	+	91.6308i	0.233053	+	0.403660i	0.958705	−	0.284402i	$-0.0917951\pi$
$227$	52.9031	+	91.6308i	0.233053	+	0.403660i	−0.725652	+	0.688062i	$0.758462\pi$
$228$	−321.925	−	108.279i	−1.41195	−	0.474910i
$229$	−64.8469	−	37.4394i	−0.283174	−	0.163491i	0.351685	−	0.936118i	$-0.385609\pi$
$229$	−64.8469	−	37.4394i	−0.283174	−	0.163491i	−0.634860	+	0.772628i	$0.718942\pi$
$230$	38.6030	+	102.134i	0.167839	+	0.444061i
$231$		0			0
$232$	84.0000	−	158.745i	0.362069	−	0.684246i
$233$	209.569	−	362.983i	0.899436	−	1.55787i	0.0712190	−	0.997461i	$-0.477311\pi$
$233$	209.569	−	362.983i	0.899436	−	1.55787i	0.828217	−	0.560408i	$-0.189356\pi$
$234$	−6.37334	−	5.21563i	−0.0272365	−	0.0222890i
$235$	−28.0000	−	48.4974i	−0.119149	−	0.206372i
$236$	48.7088	+	241.359i	0.206393	+	1.02271i
$237$			132.132i			0.557518i
$238$		0			0
$239$			148.318i			0.620577i	0.950642	+	0.310288i	$0.100426\pi$
$239$			148.318i			0.620577i	−0.950642	+	0.310288i	$0.899574\pi$
$240$	51.1652	−	67.4546i	0.213188	−	0.281061i
$241$	−229.936	−	398.261i	−0.954092	−	1.65254i	−0.736433	−	0.676510i	$-0.763492\pi$
$241$	−229.936	−	398.261i	−0.954092	−	1.65254i	−0.217658	−	0.976025i	$-0.569842\pi$
$242$	−127.781	+	156.144i	−0.528019	+	0.645224i
$243$	−69.5894	+	120.532i	−0.286376	+	0.496018i
$244$	99.6985	+	113.047i	0.408600	+	0.463309i
$245$		0			0
$246$	−65.1127	−	172.272i	−0.264686	−	0.700293i
$247$	33.3807	+	19.2724i	0.135145	+	0.0780258i
$248$	373.471	−	13.7888i	1.50593	−	0.0555998i
$249$	−6.17157	−	10.6895i	−0.0247854	−	0.0429296i
$250$	23.8306	−	145.602i	0.0953226	−	0.582407i
$251$	−124.919			−0.497685			−0.248842	−	0.968544i	$-0.580050\pi$
$251$	−124.919			−0.497685			−0.248842	+	0.968544i	$0.580050\pi$
$252$		0			0
$253$			157.993i			0.624478i
$254$	−40.3882	+	246.766i	−0.159009	+	0.971519i
$255$	108.409	−	62.5902i	0.425135	−	0.245452i
$256$	69.0091	+	246.523i	0.269567	+	0.962982i
$257$	−213.676	+	370.098i	−0.831425	+	1.44007i	0.0654835	+	0.997854i	$0.479141\pi$
$257$	−213.676	+	370.098i	−0.831425	+	1.44007i	−0.896908	+	0.442216i	$0.854192\pi$
$258$	41.4558	+	109.682i	0.160682	+	0.425123i
$259$		0			0
$260$	−7.20606	+	6.35515i	−0.0277156	+	0.0244429i
$261$	−51.6552	−	29.8231i	−0.197912	−	0.114265i
$262$	−127.107	+	155.321i	−0.485141	+	0.592828i
$263$	223.109	−	128.812i	0.848322	−	0.489779i	−0.0117625	−	0.999931i	$-0.503744\pi$
$263$	223.109	−	128.812i	0.848322	−	0.489779i	0.860084	+	0.510152i	$0.170411\pi$
$264$	103.764	−	65.1276i	0.393046	−	0.246695i
$265$	151.598			0.572068
$266$		0			0
$267$	150.426			0.563395
$268$	26.4073	+	130.852i	0.0985348	+	0.488255i
$269$	186.408	−	107.623i	0.692968	−	0.400085i	−0.111755	−	0.993736i	$-0.535647\pi$
$269$	186.408	−	107.623i	0.692968	−	0.400085i	0.804723	+	0.593650i	$0.202314\pi$
$270$	51.9511	+	42.5142i	0.192412	+	0.157460i
$271$	327.833	+	189.275i	1.20972	+	0.698431i	0.962698	−	0.270580i	$-0.0872154\pi$
$271$	327.833	+	189.275i	1.20972	+	0.698431i	0.247020	+	0.969010i	$0.420549\pi$
$272$	−47.3137	+	375.541i	−0.173947	+	1.38067i
$273$		0			0
$274$	40.5269	+	107.224i	0.147908	+	0.391329i
$275$	50.6791	−	87.7789i	0.184288	−	0.319196i
$276$	−153.362	+	455.959i	−0.555659	+	1.65202i
$277$	−144.149	+	83.2243i	−0.520393	+	0.300449i	−0.737095	−	0.675789i	$-0.763803\pi$
$277$	−144.149	+	83.2243i	−0.520393	+	0.300449i	0.216703	+	0.976238i	$0.430470\pi$
$278$	−362.505	−	59.3312i	−1.30397	−	0.213421i
$279$		−	124.117i		−	0.444863i
$280$		0			0
$281$	−421.765			−1.50094			−0.750471	−	0.660904i	$-0.770173\pi$
$281$	−421.765			−1.50094			−0.750471	+	0.660904i	$0.770173\pi$
$282$	39.8519	−	243.489i	0.141319	−	0.863437i
$283$	−172.719	−	299.159i	−0.610316	−	1.05710i	−0.991187	−	0.132470i	$-0.957709\pi$
$283$	−172.719	−	299.159i	−0.610316	−	1.05710i	0.380872	−	0.924628i	$-0.375624\pi$
$284$	130.324	−	387.464i	0.458886	−	1.36431i
$285$	113.969	+	65.8000i	0.399891	+	0.230877i
$286$	−13.0051	+	4.91545i	−0.0454722	+	0.0171869i
$287$		0			0
$288$	82.6619	−	19.8821i	0.287021	−	0.0690350i
$289$	−135.323	+	234.387i	−0.468247	+	0.811028i
$290$	−44.0711	+	53.8536i	−0.151969	+	0.185702i
$291$	−164.066	−	284.171i	−0.563801	−	0.976532i
$292$	54.8471	+	271.776i	0.187833	+	0.930739i
$293$		−	511.038i		−	1.74416i	−0.489365	−	0.872079i	$-0.662771\pi$
$293$		−	511.038i		−	1.74416i	0.489365	−	0.872079i	$-0.337229\pi$
$294$		0			0
$295$		−	95.4028i		−	0.323399i
$296$	249.146	+	396.950i	0.841708	+	1.34105i
$297$	48.5685	+	84.1232i	0.163530	+	0.283243i
$298$	−297.655	−	243.586i	−0.998841	−	0.817402i
$299$	27.2965	−	47.2789i	0.0912925	−	0.158123i
$300$	231.463	−	204.131i	0.771543	−	0.680437i
$301$		0			0
$302$	−214.683	+	81.1427i	−0.710872	+	0.268684i
$303$	58.0010	+	33.4869i	0.191422	+	0.110518i
$304$	−366.777	+	154.324i	−1.20650	+	0.507644i
$305$	−29.2010	−	50.5776i	−0.0957410	−	0.165828i
$306$	124.055	+	20.3041i	0.405409	+	0.0663532i
$307$	−223.331			−0.727462			−0.363731	−	0.931504i	$-0.618497\pi$
$307$	−223.331			−0.727462			−0.363731	+	0.931504i	$0.618497\pi$
$308$		0			0
$309$		−	147.098i		−	0.476047i
$310$	−142.903	−	23.3889i	−0.460976	−	0.0754480i
$311$	10.7376	−	6.19938i	0.0345262	−	0.0199337i	−0.482638	−	0.875820i	$-0.660321\pi$
$311$	10.7376	−	6.19938i	0.0345262	−	0.0199337i	0.517164	+	0.855886i	$0.326988\pi$
$312$	−42.3032	+	1.56186i	−0.135587	+	0.00500596i
$313$	205.024	−	355.113i	0.655030	−	1.13455i	−0.326856	−	0.945074i	$-0.605989\pi$
$313$	205.024	−	355.113i	0.655030	−	1.13455i	0.981886	−	0.189471i	$-0.0606774\pi$
$314$	396.889	−	150.010i	1.26398	−	0.477739i
$315$		0			0
$316$	102.392	+	116.102i	0.324025	+	0.367410i
$317$	112.857	+	65.1580i	0.356016	+	0.205546i	0.667332	−	0.744761i	$-0.267436\pi$
$317$	112.857	+	65.1580i	0.356016	+	0.205546i	−0.311316	+	0.950306i	$0.600770\pi$
$318$	516.900	+	423.006i	1.62547	+	1.33021i
$319$	−87.2038	+	50.3472i	−0.273366	+	0.157828i
$320$	−7.31434	−	98.9200i	−0.0228573	−	0.309125i
$321$	−53.2548			−0.165903
$322$		0			0
$323$	−588.347			−1.82151
$324$	77.4297	+	383.676i	0.238981	+	1.18419i
$325$	−30.3311	+	17.5117i	−0.0933266	+	0.0538821i
$326$	−304.668	+	372.295i	−0.934565	+	1.14201i
$327$	−11.3890	−	6.57544i	−0.0348287	−	0.0201084i
$328$	−190.711	−	100.915i	−0.581435	−	0.307666i
$329$		0			0
$330$	−44.4020	+	16.7824i	−0.134552	+	0.0508557i
$331$	−107.130	+	185.555i	−0.323655	+	0.560588i	−0.981239	−	0.192794i	$-0.938245\pi$
$331$	−107.130	+	185.555i	−0.323655	+	0.560588i	0.657584	+	0.753381i	$0.271579\pi$
$332$	−13.7064	−	4.61014i	−0.0412842	−	0.0138859i
$333$	134.793	−	77.8227i	0.404783	−	0.233702i
$334$	−68.5174	+	418.631i	−0.205142	+	1.25339i
$335$		−	51.7223i		−	0.154395i
$336$		0			0
$337$	164.049			0.486792			0.243396	−	0.969927i	$-0.421739\pi$
$337$	164.049			0.486792			0.243396	+	0.969927i	$0.421739\pi$
$338$	−328.821	−	53.8181i	−0.972843	−	0.159225i
$339$	−23.5147	−	40.7287i	−0.0693650	−	0.120144i
$340$	46.7545	−	139.006i	0.137513	−	0.408840i
$341$	−181.461	−	104.766i	−0.532143	−	0.307233i
$342$	46.7229	+	123.617i	0.136617	+	0.361454i
$343$		0			0
$344$	121.421	+	64.2501i	0.352969	+	0.186774i
$345$	93.1960	−	161.420i	0.270133	−	0.467884i
$346$	−282.027	−	230.797i	−0.815107	−	0.667043i
$347$	54.8457	+	94.9955i	0.158057	+	0.273762i	0.934168	−	0.356834i	$-0.116144\pi$
$347$	54.8457	+	94.9955i	0.158057	+	0.273762i	−0.776111	+	0.630596i	$0.782810\pi$
$348$	−300.537	+	60.6513i	−0.863611	+	0.174285i
$349$		−	463.479i		−	1.32802i	−0.747723	−	0.664010i	$-0.768853\pi$
$349$		−	463.479i		−	1.32802i	0.747723	−	0.664010i	$-0.231147\pi$
$350$		0			0
$351$		−	33.5648i		−	0.0956261i
$352$	40.7067	−	137.636i	0.115644	−	0.391010i
$353$	39.0488	+	67.6345i	0.110620	+	0.191599i	0.916020	−	0.401132i	$-0.131383\pi$
$353$	39.0488	+	67.6345i	0.110620	+	0.191599i	−0.805401	+	0.592731i	$0.798050\pi$
$354$	266.204	−	325.293i	0.751988	−	0.918907i
$355$	−79.1960	+	137.171i	−0.223087	+	0.386398i
$356$	132.177	−	116.569i	0.371283	−	0.327441i
$357$		0			0
$358$	40.4508	+	107.023i	0.112991	+	0.298946i
$359$	316.198	+	182.557i	0.880774	+	0.508515i	0.870913	−	0.491437i	$-0.163528\pi$
$359$	316.198	+	182.557i	0.880774	+	0.508515i	0.00986020	+	0.999951i	$0.496861\pi$
$360$	−32.9193	+	1.21540i	−0.0914424	+	0.00337611i
$361$	−128.760	−	223.019i	−0.356676	−	0.617780i
$362$	105.380	−	643.857i	0.291105	−	1.77861i
$363$	344.434			0.948853
$364$		0			0
$365$		−	107.426i		−	0.294316i
$366$	41.5613	−	253.933i	0.113555	−	0.693807i
$367$	−191.165	+	110.369i	−0.520887	+	0.300734i	−0.737297	−	0.675568i	$-0.763898\pi$
$367$	−191.165	+	110.369i	−0.520887	+	0.300734i	0.216411	+	0.976302i	$0.430565\pi$
$368$	218.577	+	519.485i	0.593959	+	1.41164i
$369$	−35.8284	+	62.0567i	−0.0970960	+	0.168175i
$370$	−64.2010	−	169.860i	−0.173516	−	0.459081i
$371$		0			0
$372$	−421.990	−	478.492i	−1.13438	−	1.28627i
$373$	−217.852	−	125.777i	−0.584052	−	0.337203i	0.178690	−	0.983905i	$-0.442814\pi$
$373$	−217.852	−	125.777i	−0.584052	−	0.337203i	−0.762742	+	0.646703i	$0.776147\pi$
$374$	134.399	−	164.232i	0.359356	−	0.439123i
$375$	−218.121	+	125.932i	−0.581657	+	0.335820i
$376$	−153.668	−	244.831i	−0.408692	−	0.651147i
$377$	34.7939			0.0922916
$378$		0			0
$379$	286.024			0.754682			0.377341	−	0.926074i	$-0.376839\pi$
$379$	286.024			0.754682			0.377341	+	0.926074i	$0.376839\pi$
$380$	151.132	−	30.5000i	0.397716	−	0.0802631i
$381$	369.672	−	213.430i	0.970268	−	0.560184i
$382$	−150.233	−	122.943i	−0.393279	−	0.321840i
$383$	−92.5727	−	53.4468i	−0.241704	−	0.139548i	0.374256	−	0.927326i	$-0.377898\pi$
$383$	−92.5727	−	53.4468i	−0.241704	−	0.139548i	−0.615960	+	0.787778i	$0.711232\pi$
$384$	251.078	−	357.695i	0.653850	−	0.931497i
$385$		0			0
$386$	111.230	+	294.288i	0.288162	+	0.762404i
$387$	22.8112	−	39.5101i	0.0589436	−	0.102093i
$388$	−364.372	−	122.557i	−0.939102	−	0.315867i
$389$	66.8405	−	38.5904i	0.171826	−	0.0992040i	−0.411620	−	0.911355i	$-0.635037\pi$
$389$	66.8405	−	38.5904i	0.171826	−	0.0992040i	0.583447	+	0.812151i	$0.301704\pi$
$390$	16.1866	+	2.64927i	0.0415042	+	0.00679300i
$391$			833.307i			2.13122i
$392$		0			0
$393$	342.617			0.871800
$394$	40.0949	−	244.974i	0.101764	−	0.621761i
$395$	−29.9899	−	51.9440i	−0.0759238	−	0.131504i
$396$	−45.1798	−	15.1962i	−0.114090	−	0.0383743i
$397$	−569.424	−	328.757i	−1.43432	−	0.828103i	−0.436870	−	0.899525i	$-0.643913\pi$
$397$	−569.424	−	328.757i	−1.43432	−	0.828103i	−0.997446	+	0.0714218i	$0.977246\pi$
$398$	−338.573	+	127.968i	−0.850685	+	0.321529i
$399$		0			0
$400$	45.1960	−	358.732i	0.112990	−	0.896830i
$401$	−159.397	+	276.084i	−0.397499	+	0.688488i	−0.993417	−	0.114557i	$-0.963455\pi$
$401$	−159.397	+	276.084i	−0.397499	+	0.688488i	0.595918	+	0.803045i	$0.296788\pi$
$402$	144.321	−	176.357i	0.359009	−	0.438698i
$403$	36.2010	+	62.7020i	0.0898288	+	0.155588i
$404$	76.9140	−	15.5220i	0.190381	−	0.0384209i
$405$		−	151.657i		−	0.374461i
$406$		0			0
$407$		−	262.759i		−	0.645600i
$408$	547.287	−	343.504i	1.34139	−	0.841923i
$409$	72.6325	+	125.803i	0.177585	+	0.307587i	0.941053	−	0.338259i	$-0.109838\pi$
$409$	72.6325	+	125.803i	0.177585	+	0.307587i	−0.763468	+	0.645846i	$0.776505\pi$
$410$	64.6978	+	52.9455i	0.157799	+	0.129135i
$411$	97.8406	−	169.465i	0.238055	−	0.412323i
$412$	−113.990	−	129.252i	−0.276675	−	0.313719i
$413$		0			0
$414$	175.085	−	66.1760i	0.422911	−	0.159846i
$415$	4.85237	+	2.80152i	0.0116925	+	0.00675065i
$416$	−35.9606	+	34.1541i	−0.0864438	+	0.0821012i
$417$	313.534	+	543.057i	0.751880	+	1.30229i
$418$	220.169	+	36.0351i	0.526720	+	0.0862083i
$419$	−707.012			−1.68738			−0.843690	−	0.536831i	$-0.819621\pi$
$419$	−707.012			−1.68738			−0.843690	+	0.536831i	$0.819621\pi$
$420$		0			0
$421$		−	121.989i		−	0.289761i	−0.989449	−	0.144880i	$-0.953720\pi$
$421$		−	121.989i		−	0.289761i	0.989449	−	0.144880i	$-0.0462798\pi$
$422$	−323.789	−	52.9946i	−0.767273	−	0.125580i
$423$	−83.1377	+	47.9996i	−0.196543	+	0.113474i
$424$	781.987	−	28.8714i	1.84431	−	0.0680929i
$425$	267.299	−	462.975i	0.628938	−	1.08935i
$426$	−652.784	+	246.729i	−1.53236	+	0.579176i
$427$		0			0
$428$	−46.7939	+	41.2684i	−0.109332	+	0.0964214i
$429$	20.5541	+	11.8669i	0.0479118	+	0.0276619i
$430$	−41.1917	−	33.7092i	−0.0957946	−	0.0783936i
$431$	509.969	−	294.431i	1.18322	−	0.683133i	0.226464	−	0.974020i	$-0.427283\pi$
$431$	509.969	−	294.431i	1.18322	−	0.683133i	0.956758	+	0.290886i	$0.0939501\pi$
$432$	276.076	+	209.407i	0.639064	+	0.484738i
$433$	−137.696			−0.318004			−0.159002	−	0.987278i	$-0.550828\pi$
$433$	−137.696			−0.318004			−0.159002	+	0.987278i	$0.550828\pi$
$434$		0			0
$435$	118.794			0.273090
$436$	−15.1027	+	3.04788i	−0.0346393	+	0.00699056i
$437$	−758.675	+	438.021i	−1.73610	+	1.00234i
$438$	299.751	−	366.287i	0.684362	−	0.836271i
$439$	381.522	+	220.272i	0.869070	+	0.501758i	0.867039	−	0.498240i	$-0.166020\pi$
$439$	381.522	+	220.272i	0.869070	+	0.501758i	0.00203069	+	0.999998i	$0.499354\pi$
$440$	−26.0101	+	49.1545i	−0.0591139	+	0.111715i
$441$		0			0
$442$	−68.5929	+	25.9257i	−0.155188	+	0.0586554i
$443$	243.529	−	421.805i	0.549727	−	0.952155i	−0.448566	−	0.893750i	$-0.648065\pi$
$443$	243.529	−	421.805i	0.549727	−	0.952155i	0.998293	−	0.0584052i	$-0.0186015\pi$
$444$	255.057	−	758.309i	0.574453	−	1.70790i
$445$	−59.1361	+	34.1422i	−0.132890	+	0.0767241i
$446$	3.41875	−	20.8881i	0.00766537	−	0.0468343i
$447$			656.587i			1.46887i
$448$		0			0
$449$	264.039			0.588059			0.294030	−	0.955796i	$-0.405004\pi$
$449$	264.039			0.588059			0.294030	+	0.955796i	$0.405004\pi$
$450$	−118.502	−	19.3953i	−0.263339	−	0.0431006i
$451$	60.4853	+	104.764i	0.134114	+	0.232292i
$452$	−52.2235	−	17.5654i	−0.115539	−	0.0388615i
$453$	339.301	+	195.896i	0.749010	+	0.432441i
$454$	−74.8162	−	197.945i	−0.164793	−	0.436003i
$455$		0			0
$456$	600.416	+	317.710i	1.31670	+	0.696733i
$457$	257.161	−	445.417i	0.562717	−	0.974654i	−0.434542	−	0.900652i	$-0.643090\pi$
$457$	257.161	−	445.417i	0.562717	−	0.974654i	0.997258	−	0.0740019i	$-0.0235771\pi$
$458$	115.896	+	94.8438i	0.253049	+	0.207083i
$459$	256.167	+	443.693i	0.558097	+	0.966652i
$460$	−43.1987	−	214.056i	−0.0939103	−	0.465340i
$461$		−	202.224i		−	0.438664i	−0.975650	−	0.219332i	$-0.929612\pi$
$461$		−	202.224i		−	0.438664i	0.975650	−	0.219332i	$-0.0703878\pi$
$462$		0			0
$463$			722.653i			1.56081i	0.625277	+	0.780403i	$0.284986\pi$
$463$			722.653i			1.56081i	−0.625277	+	0.780403i	$0.715014\pi$
$464$	−217.075	+	286.186i	−0.467835	+	0.616780i
$465$	123.598	+	214.078i	0.265802	+	0.460383i
$466$	−530.892	+	648.735i	−1.13925	+	1.39213i
$467$	−173.641	+	300.755i	−0.371822	+	0.644015i	−0.989846	−	0.142144i	$-0.954600\pi$
$467$	−173.641	+	300.755i	−0.371822	+	0.644015i	0.618023	+	0.786160i	$0.287934\pi$
$468$	10.8944	+	12.3531i	0.0232787	+	0.0263956i
$469$		0			0
$470$	39.5980	+	104.766i	0.0842510	+	0.222907i
$471$	−627.273	−	362.156i	−1.33179	−	0.768910i
$472$	−18.1692	−	492.115i	−0.0384940	−	1.04262i
$473$	−38.5097	−	66.7007i	−0.0814158	−	0.141016i
$474$	42.6841	−	260.794i	0.0900509	−	0.550198i
$475$	562.013			1.18319
$476$		0			0
$477$		−	259.880i		−	0.544822i
$478$	47.9129	−	292.741i	0.100236	−	0.612428i
$479$	25.2716	−	14.5906i	0.0527591	−	0.0304605i	−0.473388	−	0.880854i	$-0.656969\pi$
$479$	25.2716	−	14.5906i	0.0527591	−	0.0304605i	0.526148	+	0.850393i	$0.323636\pi$
$480$	−122.777	+	116.609i	−0.255786	+	0.242936i
$481$	−45.3970	+	78.6299i	−0.0943804	+	0.163472i
$482$	325.179	+	860.342i	0.674645	+	1.78494i
$483$		0			0
$484$	302.647	−	266.909i	0.625303	−	0.551466i
$485$	128.996	+	74.4760i	0.265972	+	0.153559i
$486$	176.288	−	215.419i	0.362733	−	0.443249i
$487$	−607.640	+	350.821i	−1.24772	+	0.720372i	−0.970654	−	0.240478i	$-0.922696\pi$
$487$	−607.640	+	350.821i	−1.24772	+	0.720372i	−0.277067	+	0.960851i	$0.589362\pi$
$488$	−160.260	−	255.333i	−0.328401	−	0.523223i
$489$	821.235			1.67942
$490$		0			0
$491$	−59.9512			−0.122100			−0.0610501	−	0.998135i	$-0.519445\pi$
$491$	−59.9512			−0.122100			−0.0610501	+	0.998135i	$0.519445\pi$
$492$	72.8644	+	361.054i	0.148098	+	0.733850i
$493$	−459.942	+	265.548i	−0.932945	+	0.538636i
$494$	−59.6590	−	48.8220i	−0.120767	−	0.0988299i
$495$	15.9947	+	9.23455i	0.0323125	+	0.0186557i
$496$	−741.588	−	93.4313i	−1.49514	−	0.188370i
$497$		0			0
$498$	8.72792	+	23.0919i	0.0175259	+	0.0463693i
$499$	42.1421	−	72.9923i	0.0844532	−	0.146277i	−0.820705	−	0.571352i	$-0.806419\pi$
$499$	42.1421	−	72.9923i	0.0844532	−	0.146277i	0.905158	+	0.425075i	$0.139752\pi$
$500$	−94.0709	+	279.681i	−0.188142	+	0.559363i
$501$	627.138	−	362.079i	1.25177	−	0.722712i
$502$	246.557	+	40.3540i	0.491150	+	0.0803865i
$503$			409.987i			0.815083i	0.913187	+	0.407542i	$0.133614\pi$
$503$			409.987i			0.815083i	−0.913187	+	0.407542i	$0.866386\pi$
$504$		0			0
$505$	−30.4020			−0.0602020
$506$	51.0384	−	311.837i	0.100866	−	0.616278i
$507$	284.401	+	492.596i	0.560948	+	0.971590i
$508$	159.431	−	474.004i	0.313841	−	0.933079i
$509$	−413.123	−	238.516i	−0.811636	−	0.468598i	0.0358878	−	0.999356i	$-0.488574\pi$
$509$	−413.123	−	238.516i	−0.811636	−	0.468598i	−0.847524	+	0.530758i	$0.821907\pi$
$510$	−234.191	+	88.5158i	−0.459198	+	0.173560i
$511$		0			0
$512$	−56.5685	−	508.865i	−0.110485	−	0.993878i
$513$	−269.304	+	466.448i	−0.524958	+	0.909254i
$514$	541.298	−	661.450i	1.05311	−	1.28687i
$515$	33.3869	+	57.8278i	0.0648289	+	0.112287i
$516$	−46.3912	−	229.875i	−0.0899054	−	0.445495i
$517$			162.065i			0.313472i
$518$		0			0
$519$			622.114i			1.19868i
$520$	16.2759	−	10.2155i	0.0312997	−	0.0196453i
$521$	105.437	+	182.621i	0.202373	+	0.350521i	0.949293	−	0.314394i	$-0.101801\pi$
$521$	105.437	+	182.621i	0.202373	+	0.350521i	−0.746919	+	0.664915i	$0.768468\pi$
$522$	92.3196	+	75.5498i	0.176858	+	0.144731i
$523$	255.783	−	443.030i	0.489069	−	0.847093i	−0.510852	−	0.859669i	$-0.670670\pi$
$523$	255.783	−	443.030i	0.489069	−	0.847093i	0.999921	+	0.0125761i	$0.00400319\pi$
$524$	301.051	−	265.502i	0.574525	−	0.506683i
$525$		0			0
$526$	−481.970	+	182.167i	−0.916292	+	0.346326i
$527$	−957.084	−	552.573i	−1.81610	−	1.04852i
$528$	−225.842	+	95.0247i	−0.427732	+	0.179971i
$529$	355.892	+	616.423i	0.672764	+	1.16526i
$530$	−299.215	−	48.9725i	−0.564556	−	0.0924009i
$531$	−163.546			−0.307997
$532$		0			0
$533$		−	41.8002i		−	0.0784244i
$534$	−296.902	−	48.5940i	−0.555997	−	0.0910001i
$535$	20.9357	−	12.0872i	0.0391321	−	0.0225929i
$536$	−9.85037	−	266.799i	−0.0183776	−	0.497759i
$537$	97.6569	−	169.147i	0.181856	−	0.314984i
$538$	−402.688	+	152.202i	−0.748491	+	0.282903i
$539$		0			0
$540$	−88.8040	−	100.694i	−0.164452	−	0.186471i
$541$	296.542	+	171.208i	0.548136	+	0.316466i	0.748370	−	0.663282i	$-0.230837\pi$
$541$	296.542	+	171.208i	0.548136	+	0.316466i	−0.200234	+	0.979748i	$0.564170\pi$
$542$	−585.914	−	479.483i	−1.08102	−	0.884654i
$543$	−964.542	+	556.878i	−1.77632	+	1.02556i
$544$	214.700	−	725.935i	0.394670	−	1.33444i
$545$	5.96970			0.0109536
$546$		0			0
$547$	−441.976			−0.807999			−0.404000	−	0.914759i	$-0.632380\pi$
$547$	−441.976			−0.807999			−0.404000	+	0.914759i	$0.632380\pi$
$548$	−45.3516	−	224.724i	−0.0827585	−	0.410081i
$549$	−86.7038	+	50.0584i	−0.157930	+	0.0911811i
$550$	−128.384	+	156.881i	−0.233425	+	0.285238i
$551$	−483.529	−	279.166i	−0.877548	−	0.506653i
$552$	449.990	−	850.401i	0.815199	−	1.54058i
$553$		0			0
$554$	311.397	−	117.697i	0.562088	−	0.212449i
$555$	−154.995	+	268.459i	−0.279270	+	0.483710i
$556$	696.323	+	234.208i	1.25238	+	0.421238i
$557$	−316.714	+	182.855i	−0.568607	+	0.328285i	−0.756593	−	0.653886i	$-0.773137\pi$
$557$	−316.714	+	182.855i	−0.568607	+	0.328285i	0.187986	+	0.982172i	$0.439804\pi$
$558$	−40.0949	+	244.974i	−0.0718546	+	0.439021i
$559$			26.6133i			0.0476087i
$560$		0			0
$561$	−362.274			−0.645765
$562$	832.453	+	136.248i	1.48123	+	0.242433i
$563$	403.194	+	698.353i	0.716154	+	1.24041i	0.962513	+	0.271236i	$0.0874323\pi$
$563$	403.194	+	698.353i	0.716154	+	1.24041i	−0.246359	+	0.969179i	$0.579234\pi$
$564$	−157.315	+	467.711i	−0.278926	+	0.829274i
$565$	18.4883	+	10.6743i	0.0327227	+	0.0188925i
$566$	244.262	+	646.256i	0.431558	+	1.14180i
$567$		0			0
$568$	−382.392	+	722.653i	−0.673225	+	1.27228i
$569$	−111.446	+	193.030i	−0.195862	+	0.339244i	−0.947183	−	0.320694i	$-0.896084\pi$
$569$	−111.446	+	193.030i	−0.195862	+	0.339244i	0.751320	+	0.659938i	$0.229417\pi$
$570$	−203.689	−	166.689i	−0.357349	−	0.292436i
$571$	−286.541	−	496.304i	−0.501823	−	0.869184i	−0.999998	−	0.00210683i	$-0.999329\pi$
$571$	−286.541	−	496.304i	−0.501823	−	0.869184i	0.498174	−	0.867077i	$-0.334004\pi$
$572$	27.2565	−	5.50063i	0.0476512	−	0.00961649i
$573$			331.393i			0.578348i
$574$		0			0
$575$		−	796.008i		−	1.38436i
$576$	−169.576	+	12.5388i	−0.294402	+	0.0217687i
$577$	−361.950	−	626.916i	−0.627297	−	1.08651i	−0.988092	−	0.153865i	$-0.950828\pi$
$577$	−361.950	−	626.916i	−0.627297	−	1.08651i	0.360795	−	0.932645i	$-0.382505\pi$
$578$	342.810	−	418.903i	0.593097	−	0.724746i
$579$	268.534	−	465.115i	0.463789	−	0.803307i
$580$	104.382	−	92.0561i	0.179969	−	0.158717i
$581$		0			0
$582$	232.024	+	613.879i	0.398667	+	1.05477i
$583$	−379.949	−	219.364i	−0.651714	−	0.376267i
$584$	−20.4589	−	554.132i	−0.0350323	−	0.948856i
$585$	−3.19091	−	5.52682i	−0.00545455	−	0.00944755i
$586$	−165.087	+	1008.66i	−0.281718	+	1.72126i
$587$	−21.1198			−0.0359793			−0.0179896	−	0.999838i	$-0.505727\pi$
$587$	−21.1198			−0.0359793			−0.0179896	+	0.999838i	$0.505727\pi$
$588$		0			0
$589$		−	1161.82i		−	1.97253i
$590$	−30.8191	+	188.300i	−0.0522358	+	0.319153i
$591$	−366.988	+	211.880i	−0.620960	+	0.358512i
$592$	−363.517	−	863.960i	−0.614049	−	1.45939i
$593$	−64.3726	+	111.497i	−0.108554	+	0.188021i	−0.915185	−	0.403035i	$-0.867955\pi$
$593$	−64.3726	+	111.497i	−0.108554	+	0.188021i	0.806631	+	0.591056i	$0.201289\pi$
$594$	−68.6863	−	181.727i	−0.115633	−	0.305937i
$595$		0			0
$596$	508.804	+	576.930i	0.853698	+	0.968003i
$597$	535.105	+	308.943i	0.896324	+	0.517493i
$598$	−69.1491	+	84.4982i	−0.115634	+	0.141301i
$599$	280.705	−	162.065i	0.468623	−	0.270559i	−0.247040	−	0.969005i	$-0.579458\pi$
$599$	280.705	−	162.065i	0.468623	−	0.270559i	0.715663	+	0.698446i	$0.246125\pi$
$600$	−522.790	+	328.129i	−0.871317	+	0.546882i
$601$	721.862			1.20110			0.600551	−	0.799587i	$-0.294948\pi$
$601$	721.862			1.20110			0.600551	+	0.799587i	$0.294948\pi$
$602$		0			0
$603$	−88.6661			−0.147042
$604$	449.941	−	90.8027i	0.744936	−	0.150336i
$605$	−135.405	+	78.1759i	−0.223809	+	0.129216i
$606$	−103.661	−	84.8311i	−0.171058	−	0.139985i
$607$	611.413	+	353.000i	1.00727	+	0.581548i	0.910391	−	0.413748i	$-0.135781\pi$
$607$	611.413	+	353.000i	1.00727	+	0.581548i	0.0968795	+	0.995296i	$0.469114\pi$
$608$	773.775	−	186.110i	1.27266	−	0.306103i
$609$		0			0
$610$	41.2965	+	109.260i	0.0676991	+	0.179115i
$611$	28.0000	−	48.4974i	0.0458265	−	0.0793739i
$612$	−238.293	−	80.1499i	−0.389368	−	0.130964i
$613$	18.9026	−	10.9134i	0.0308363	−	0.0178033i	−0.484503	−	0.874790i	$-0.660999\pi$
$613$	18.9026	−	10.9134i	0.0308363	−	0.0178033i	0.515339	+	0.856986i	$0.327666\pi$
$614$	440.797	+	72.1453i	0.717910	+	0.117500i
$615$		−	142.715i		−	0.232057i
$616$		0			0
$617$	−699.578			−1.13384			−0.566919	−	0.823774i	$-0.691865\pi$
$617$	−699.578			−1.13384			−0.566919	+	0.823774i	$0.691865\pi$
$618$	−47.5190	+	290.334i	−0.0768915	+	0.469796i
$619$	48.0990	+	83.3100i	0.0777044	+	0.134588i	0.902259	−	0.431194i	$-0.141908\pi$
$619$	48.0990	+	83.3100i	0.0777044	+	0.134588i	−0.824555	+	0.565782i	$0.808574\pi$
$620$	274.497	+	92.3271i	0.442737	+	0.148915i
$621$	660.654	+	381.429i	1.06386	+	0.614217i
$622$	−23.1960	+	8.76725i	−0.0372925	+	0.0140953i
$623$		0			0
$624$	84.0000	+	10.5830i	0.134615	+	0.0169599i
$625$	−225.309	+	390.247i	−0.360495	+	0.624395i
$626$	−519.381	+	634.668i	−0.829682	+	1.01385i
$627$	−190.426	−	329.828i	−0.303710	−	0.526042i
$628$	−831.815	+	167.869i	−1.32455	+	0.267307i
$629$		−	1385.88i		−	2.20331i
$630$		0			0
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	−164.589	−	262.231i	−0.260426	−	0.414922i
$633$	280.049	+	485.059i	0.442415	+	0.766285i
$634$	−201.701	−	165.062i	−0.318141	−	0.260351i
$635$	−96.8843	+	167.809i	−0.152574	+	0.264266i
$636$	−883.578	−	1001.88i	−1.38927	−	1.57529i
$637$		0			0
$638$	188.382	−	71.2016i	0.295269	−	0.111601i
$639$	235.149	+	135.763i	0.367995	+	0.212462i
$640$	−17.5187	+	197.605i	−0.0273730	+	0.308758i
$641$	−317.907	−	550.630i	−0.495954	−	0.859018i	0.504035	−	0.863683i	$-0.331848\pi$
$641$	−317.907	−	550.630i	−0.495954	−	0.859018i	−0.999989	+	0.00466541i	$0.998515\pi$
$642$	105.111	+	17.2035i	0.163724	+	0.0267968i
$643$	−1281.70			−1.99332			−0.996658	−	0.0816828i	$-0.973971\pi$
$643$	−1281.70			−1.99332			−0.996658	+	0.0816828i	$0.973971\pi$
$644$		0			0
$645$			90.8634i			0.140874i
$646$	1161.24	+	190.061i	1.79759	+	0.294212i
$647$	225.826	−	130.381i	0.349035	−	0.201516i	−0.315225	−	0.949017i	$-0.602080\pi$
$647$	225.826	−	130.381i	0.349035	−	0.201516i	0.664260	+	0.747501i	$0.268747\pi$
$648$	−28.8826	−	782.290i	−0.0445719	−	1.20724i
$649$	−138.049	+	239.107i	−0.212710	+	0.368424i
$650$	65.5227	−	24.7653i	0.100804	−	0.0381004i
$651$		0			0
$652$	721.602	−	636.393i	1.10675	−	0.976063i
$653$	944.471	+	545.291i	1.44636	+	0.835055i	0.998262	−	0.0589313i	$-0.0187693\pi$
$653$	944.471	+	545.291i	1.44636	+	0.835055i	0.448095	+	0.893986i	$0.352103\pi$
$654$	20.3547	+	16.6573i	0.0311235	+	0.0254699i
$655$	−134.691	+	77.7637i	−0.205635	+	0.118723i
$656$	343.813	+	260.787i	0.524106	+	0.397541i
$657$	−184.156			−0.280299
$658$		0			0
$659$	−362.780			−0.550500			−0.275250	−	0.961373i	$-0.588761\pi$
$659$	−362.780			−0.550500			−0.275250	+	0.961373i	$0.588761\pi$
$660$	93.0594	−	18.7803i	0.140999	−	0.0284550i
$661$	−102.047	+	58.9169i	−0.154383	+	0.0891330i	−0.575201	−	0.818012i	$-0.695076\pi$
$661$	−102.047	+	58.9169i	−0.154383	+	0.0891330i	0.420818	+	0.907145i	$0.361743\pi$
$662$	271.388	−	331.629i	0.409952	−	0.500950i
$663$	108.409	+	62.5902i	0.163513	+	0.0944045i
$664$	25.5635	+	13.5269i	0.0384992	+	0.0203719i
$665$		0			0
$666$	−291.186	+	110.058i	−0.437216	+	0.165252i
$667$	−395.397	+	684.848i	−0.592799	+	1.02676i
$668$	270.471	−	804.135i	0.404897	−	1.20379i
$669$	−31.2918	+	18.0663i	−0.0467740	+	0.0270050i
$670$	−16.7085	+	102.086i	−0.0249380	+	0.152368i
$671$			169.017i			0.251888i
$672$		0			0
$673$	−6.56854			−0.00976009			−0.00488005	−	0.999988i	$-0.501553\pi$
$673$	−6.56854			−0.00976009			−0.00488005	+	0.999988i	$0.501553\pi$
$674$	−323.789	−	52.9946i	−0.480400	−	0.0786270i
$675$	−244.701	−	423.834i	−0.362519	−	0.627902i
$676$	631.621	+	212.446i	0.934350	+	0.314269i
$677$	108.942	+	62.8978i	0.160919	+	0.0929066i	0.578297	−	0.815826i	$-0.303718\pi$
$677$	108.942	+	62.8978i	0.160919	+	0.0929066i	−0.417378	+	0.908733i	$0.637051\pi$
$678$	33.2548	+	87.9840i	0.0490484	+	0.129770i
$679$		0			0
$680$	−137.186	+	259.257i	−0.201744	+	0.381260i
$681$	−180.622	+	312.847i	−0.265231	+	0.459394i
$682$	324.312	+	265.401i	0.475531	+	0.389151i
$683$	276.887	+	479.583i	0.405399	+	0.702171i	0.994368	−	0.105984i	$-0.0337994\pi$
$683$	276.887	+	479.583i	0.405399	+	0.702171i	−0.588969	+	0.808156i	$0.700466\pi$
$684$	−52.2852	−	259.081i	−0.0764404	−	0.378774i
$685$			88.8274i			0.129675i
$686$		0			0
$687$		−	255.652i		−	0.372128i
$688$	−218.899	−	166.037i	−0.318166	−	0.241333i
$689$	75.7990	+	131.288i	0.110013	+	0.190548i
$690$	−236.090	+	288.495i	−0.342159	+	0.418109i
$691$	−523.413	+	906.577i	−0.757471	+	1.31198i	0.186665	+	0.982424i	$0.440232\pi$
$691$	−523.413	+	906.577i	−0.757471	+	1.31198i	−0.944136	+	0.329555i	$0.893101\pi$
$692$	482.090	+	546.639i	0.696662	+	0.789941i
$693$		0			0
$694$	−77.5635	−	205.214i	−0.111763	−	0.295697i
$695$	−246.515	−	142.325i	−0.354698	−	0.204785i
$696$	612.774	−	22.6240i	0.880422	−	0.0325057i
$697$	319.019	+	552.558i	0.457703	+	0.792766i
$698$	−149.723	+	914.787i	−0.214503	+	1.31058i
$699$	1431.02			2.04724
$700$		0			0
$701$		−	625.993i		−	0.893000i	−0.894784	−	0.446500i	$-0.852670\pi$
$701$		−	625.993i		−	0.893000i	0.894784	−	0.446500i	$-0.147330\pi$
$702$	−10.8428	+	66.2481i	−0.0154456	+	0.0943705i
$703$	1261.76	−	728.476i	1.79482	−	1.03624i
$704$	−124.806	+	258.507i	−0.177282	+	0.367197i
$705$	95.5980	−	165.581i	0.135600	−	0.234866i
$706$	−55.2233	−	146.107i	−0.0782200	−	0.206951i
$707$		0			0
$708$	−630.500	+	556.048i	−0.890536	+	0.785379i
$709$	−513.979	−	296.746i	−0.724935	−	0.418541i	0.0916314	−	0.995793i	$-0.470792\pi$
$709$	−513.979	−	296.746i	−0.724935	−	0.418541i	−0.816566	+	0.577252i	$0.804125\pi$
$710$	200.624	−	245.157i	0.282569	−	0.345291i
$711$	−89.0461	+	51.4108i	−0.125241	+	0.0723077i
$712$	−298.539	+	187.378i	−0.419296	+	0.263171i
$713$	−1645.55			−2.30792
$714$		0			0
$715$	−10.7737			−0.0150682
$716$	−45.2665	−	224.302i	−0.0632213	−	0.313271i
$717$	−438.546	+	253.194i	−0.611640	+	0.353130i
$718$	−565.118	−	462.465i	−0.787073	−	0.644101i
$719$	−529.578	−	305.752i	−0.736549	−	0.425247i	0.0842645	−	0.996443i	$-0.473146\pi$
$719$	−529.578	−	305.752i	−0.736549	−	0.425247i	−0.820813	+	0.571197i	$0.806479\pi$
$720$	65.3667	+	8.23543i	0.0907870	+	0.0114381i
$721$		0			0
$722$	182.094	+	481.775i	0.252208	+	0.667279i
$723$	785.051	−	1359.75i	1.08582	−	1.88070i
$724$	−415.985	+	1236.76i	−0.574566	+	1.70824i
$725$	439.355	−	253.662i	0.606007	−	0.349878i
$726$	−679.822	−	111.266i	−0.936394	−	0.153260i
$727$		−	944.144i		−	1.29868i	−0.760496	−	0.649342i	$-0.775044\pi$
$727$		−	944.144i		−	1.29868i	0.760496	−	0.649342i	$-0.224956\pi$
$728$		0			0
$729$	405.489			0.556227
$730$	−34.7029	+	212.030i	−0.0475383	+	0.290452i
$731$	−203.113	−	351.802i	−0.277856	−	0.481261i
$732$	−164.062	+	487.772i	−0.224129	+	0.666355i
$733$	−189.014	−	109.127i	−0.257863	−	0.148878i	0.365496	−	0.930813i	$-0.380899\pi$
$733$	−189.014	−	109.127i	−0.257863	−	0.148878i	−0.623360	+	0.781935i	$0.714233\pi$
$734$	412.965	−	156.086i	0.562622	−	0.212651i
$735$		0			0
$736$	−263.598	−	1095.94i	−0.358149	−	1.48905i
$737$	−74.8427	+	129.631i	−0.101550	+	0.175891i
$738$	90.7628	−	110.910i	0.122985	−	0.150284i
$739$	3.64971	+	6.32149i	0.00493872	+	0.00855411i	0.868484	−	0.495717i	$-0.165095\pi$
$739$	3.64971	+	6.32149i	0.00493872	+	0.00855411i	−0.863545	+	0.504271i	$0.831761\pi$
$740$	71.8441	+	355.999i	0.0970867	+	0.481079i
$741$			131.600i			0.177598i
$742$		0			0
$743$		−	106.867i		−	0.143832i	−0.997411	−	0.0719159i	$-0.977089\pi$
$743$		−	106.867i		−	0.143832i	0.997411	−	0.0719159i	$-0.0229113\pi$
$744$	678.325	+	1080.74i	0.911727	+	1.45260i
$745$	−149.025	−	258.119i	−0.200034	−	0.346469i
$746$	389.351	+	318.625i	0.521918	+	0.427112i
$747$	4.80256	−	8.31828i	0.00642913	−	0.0111356i
$748$	−318.323	+	280.734i	−0.425565	+	0.375313i
$749$		0			0
$750$	471.196	−	178.095i	0.628261	−	0.237460i
$751$	−110.387	−	63.7317i	−0.146986	−	0.0848624i	0.424703	−	0.905333i	$-0.360378\pi$
$751$	−110.387	−	63.7317i	−0.146986	−	0.0848624i	−0.571689	+	0.820470i	$0.693712\pi$
$752$	224.210	+	532.874i	0.298152	+	0.708609i
$753$	−213.250	−	369.359i	−0.283200	−	0.490517i
$754$	−68.6741	−	11.2399i	−0.0910798	−	0.0149070i
$755$	−177.849			−0.235562
$756$		0			0
$757$			704.275i			0.930350i	0.885219	+	0.465175i	$0.154009\pi$
$757$			704.275i			0.930350i	−0.885219	+	0.465175i	$0.845991\pi$
$758$	−564.537	−	92.3979i	−0.744772	−	0.121897i
$759$	−467.153	+	269.711i	−0.615485	+	0.355350i
$760$	−308.148	+	11.3770i	−0.405458	+	0.0149697i
$761$	−501.465	+	868.563i	−0.658955	+	1.14134i	0.321931	+	0.946763i	$0.395668\pi$
$761$	−501.465	+	868.563i	−0.658955	+	1.14134i	−0.980886	+	0.194581i	$0.937665\pi$
$762$	−798.583	+	301.836i	−1.04801	+	0.396110i
$763$		0			0
$764$	256.804	+	291.188i	0.336131	+	0.381137i
$765$	84.3614	+	48.7061i	0.110276	+	0.0636681i
$766$	165.449	+	135.395i	0.215990	+	0.176756i
$767$	82.6213	−	47.7014i	0.107720	−	0.0621922i
$768$	−611.113	+	624.887i	−0.795720	+	0.813655i
$769$	646.950			0.841288			0.420644	−	0.907226i	$-0.361804\pi$
$769$	646.950			0.841288			0.420644	+	0.907226i	$0.361804\pi$
$770$		0			0
$771$	−1459.07			−1.89244
$772$	−124.472	−	616.780i	−0.161234	−	0.798938i
$773$	488.668	−	282.132i	0.632170	−	0.364984i	−0.149422	−	0.988774i	$-0.547741\pi$
$773$	488.668	−	282.132i	0.632170	−	0.364984i	0.781592	+	0.623790i	$0.214408\pi$
$774$	−57.7867	+	70.6137i	−0.0746599	+	0.0912322i
$775$	914.245	+	527.840i	1.17967	+	0.681083i
$776$	679.584	+	359.602i	0.875752	+	0.463404i
$777$		0			0
$778$	−144.392	+	54.5750i	−0.185594	+	0.0701478i
$779$	−335.380	+	580.895i	−0.430526	+	0.745693i
$780$	−31.0924	−	10.4579i	−0.0398620	−	0.0134076i
$781$	396.977	−	229.195i	0.508293	−	0.293463i
$782$	269.193	−	1644.73i	0.344237	−	2.10324i
$783$			486.195i			0.620939i
$784$		0			0
$785$	328.794			0.418846
$786$	−676.237	−	110.680i	−0.860352	−	0.140814i
$787$	461.673	+	799.640i	0.586623	+	1.01606i	0.994671	+	0.103101i	$0.0328764\pi$
$787$	461.673	+	799.640i	0.586623	+	1.01606i	−0.408048	+	0.912961i	$0.633790\pi$
$788$	−158.274	+	470.562i	−0.200855	+	0.597160i
$789$	761.740	+	439.791i	0.965451	+	0.557403i
$790$	42.4121	+	112.212i	0.0536862	+	0.142040i
$791$		0			0
$792$	84.2641	+	44.5884i	0.106394	+	0.0562984i
$793$	29.2010	−	50.5776i	0.0368235	−	0.0637801i
$794$	1017.69	+	832.828i	1.28173	+	1.04890i
$795$	258.794	+	448.244i	0.325527	+	0.563829i
$796$	709.593	−	143.203i	0.891449	−	0.179903i
$797$			207.983i			0.260957i	0.991451	+	0.130479i	$0.0416514\pi$
$797$			207.983i			0.260957i	−0.991451	+	0.130479i	$0.958349\pi$
$798$		0			0
$799$			854.785i			1.06982i
$800$	−205.090	+	693.443i	−0.256363	+	0.866803i
$801$	58.5290	+	101.375i	0.0730699	+	0.126561i
$802$	403.795	−	493.425i	0.503484	−	0.615243i
$803$	−155.446	+	269.240i	−0.193581	+	0.335293i
$804$	−341.823	+	301.460i	−0.425153	+	0.374950i
$805$		0			0
$806$	−51.1960	−	135.452i	−0.0635186	−	0.168054i
$807$	636.438	+	367.448i	0.788647	+	0.455326i
$808$	−156.822	+	5.78998i	−0.194087	+	0.00716581i
$809$	−170.270	−	294.916i	−0.210470	−	0.364544i	0.741392	−	0.671072i	$-0.234166\pi$
$809$	−170.270	−	294.916i	−0.210470	−	0.364544i	−0.951862	+	0.306528i	$0.900833\pi$
$810$	−48.9915	+	299.331i	−0.0604833	+	0.369544i
$811$	907.380			1.11884			0.559420	−	0.828884i	$-0.311024\pi$
$811$	907.380			1.11884			0.559420	+	0.828884i	$0.311024\pi$
$812$		0			0
$813$			1292.45i			1.58973i
$814$	−84.8823	+	518.618i	−0.104278	+	0.637123i
$815$	−322.846	+	186.395i	−0.396130	+	0.228706i
$816$	−1191.17	+	501.191i	−1.45976	+	0.614205i
$817$	213.529	−	369.843i	0.261357	−	0.452684i
$818$	−102.718	−	271.766i	−0.125572	−	0.332232i
$819$		0			0
$820$	−110.593	−	125.401i	−0.134869	−	0.152928i
$821$	−548.560	−	316.711i	−0.668161	−	0.385763i	0.127219	−	0.991875i	$-0.459395\pi$
$821$	−548.560	−	316.711i	−0.668161	−	0.385763i	−0.795379	+	0.606112i	$0.792728\pi$
$822$	−247.856	+	302.873i	−0.301528	+	0.368458i
$823$	−124.404	+	71.8247i	−0.151159	+	0.0872718i	−0.573672	−	0.819085i	$-0.694482\pi$
$823$	−124.404	+	71.8247i	−0.151159	+	0.0872718i	0.422513	+	0.906357i	$0.361148\pi$
$824$	183.232	+	291.934i	0.222369	+	0.354289i
$825$	346.059			0.419465
$826$		0			0
$827$	1545.57			1.86888			0.934442	−	0.356114i	$-0.115899\pi$
$827$	1545.57			1.86888			0.934442	+	0.356114i	$0.115899\pi$
$828$	−366.950	+	74.0543i	−0.443177	+	0.0894376i
$829$	644.285	−	371.978i	0.777183	−	0.448707i	−0.0582482	−	0.998302i	$-0.518551\pi$
$829$	644.285	−	371.978i	0.777183	−	0.448707i	0.835431	+	0.549595i	$0.185218\pi$
$830$	−8.67231	−	7.09699i	−0.0104486	−	0.00855058i
$831$	−492.155	−	284.146i	−0.592244	−	0.341932i
$832$	82.0101	−	55.7944i	0.0985698	−	0.0670606i
$833$		0			0
$834$	−443.404	−	1173.14i	−0.531660	−	1.40664i
$835$	−164.362	+	284.683i	−0.196840	+	0.340937i
$836$	−422.915	−	142.248i	−0.505879	−	0.170153i
$837$	−876.170	+	505.857i	−1.04680	+	0.604369i
$838$	1395.46	+	228.395i	1.66522	+	0.272547i
$839$		−	96.3107i		−	0.114792i	−0.998351	−	0.0573961i	$-0.981720\pi$
$839$		−	96.3107i		−	0.114792i	0.998351	−	0.0573961i	$-0.0182798\pi$
$840$		0			0
$841$	337.000			0.400713
$842$	−39.4077	+	240.775i	−0.0468025	+	0.285956i
$843$	−719.997	−	1247.07i	−0.854089	−	1.47933i
$844$	621.956	+	209.195i	0.736915	+	0.247861i
$845$	−223.609	−	129.101i	−0.264626	−	0.152782i
$846$	179.598	−	67.8817i	0.212291	−	0.0802384i
$847$		0			0
$848$	−1552.76	−	195.630i	−1.83109	−	0.230696i
$849$	589.701	−	1021.39i	0.694583	−	1.20305i
$850$	−677.138	+	827.442i	−0.796633	+	0.973462i
$851$	−1031.78	−	1787.09i	−1.21243	−	2.09999i
$852$	1368.13	−	276.102i	1.60578	−	0.324064i
$853$			904.866i			1.06080i	0.847746	+	0.530402i	$0.177959\pi$
$853$			904.866i			1.06080i	−0.847746	+	0.530402i	$0.822041\pi$
$854$		0			0
$855$			102.408i			0.119775i
$856$	105.690	−	66.3366i	0.123470	−	0.0774960i
$857$	80.4659	+	139.371i	0.0938926	+	0.162627i	0.909146	−	0.416478i	$-0.136736\pi$
$857$	80.4659	+	139.371i	0.0938926	+	0.162627i	−0.815253	+	0.579105i	$0.803402\pi$
$858$	−36.7350	−	30.0621i	−0.0428147	−	0.0350374i
$859$	115.846	−	200.652i	0.134862	−	0.233587i	−0.790683	−	0.612226i	$-0.790274\pi$
$859$	115.846	−	200.652i	0.134862	−	0.233587i	0.925545	+	0.378638i	$0.123608\pi$
$860$	70.4121	+	79.8398i	0.0818746	+	0.0928370i
$861$		0			0
$862$	−1101.66	+	416.388i	−1.27803	+	0.483048i
$863$	1158.18	+	668.674i	1.34204	+	0.774825i	0.987106	−	0.160068i	$-0.0511712\pi$
$863$	1158.18	+	668.674i	1.34204	+	0.774825i	0.354931	+	0.934893i	$0.384505\pi$
$864$	−477.254	−	502.498i	−0.552377	−	0.581595i
$865$	−141.201	−	244.567i	−0.163238	−	0.282737i
$866$	271.775	+	44.4814i	0.313828	+	0.0513642i
$867$	−924.046			−1.06580
$868$		0			0
$869$			173.583i			0.199750i
$870$	−234.468	−	38.3754i	−0.269504	−	0.0441097i
$871$	44.7929	−	25.8612i	0.0514269	−	0.0296914i
$872$	30.7934	−	1.13691i	0.0353136	−	0.00130380i
$873$	127.672	−	221.134i	0.146245	−	0.253304i
$874$	1638.92	−	619.455i	1.87520	−	0.708759i
$875$		0			0
$876$	−709.955	+	626.122i	−0.810451	+	0.714751i
$877$	−1243.73	−	718.068i	−1.41816	−	0.818777i	−0.422026	−	0.906584i	$-0.638681\pi$
$877$	−1243.73	−	718.068i	−1.41816	−	0.818777i	−0.996138	+	0.0878061i	$0.972014\pi$
$878$	−681.867	−	558.006i	−0.776614	−	0.635542i
$879$	1511.04	−	872.397i	1.71904	−	0.992488i
$880$	67.2161	−	88.6157i	0.0763819	−	0.100700i
$881$	186.706			0.211926			0.105963	−	0.994370i	$-0.466208\pi$
$881$	186.706			0.211926			0.105963	+	0.994370i	$0.466208\pi$
$882$		0			0
$883$	1277.99			1.44733			0.723664	−	0.690153i	$-0.242457\pi$
$883$	1277.99			1.44733			0.723664	+	0.690153i	$0.242457\pi$
$884$	143.760	−	29.0121i	0.162624	−	0.0328192i
$885$	282.087	−	162.863i	0.318742	−	0.184026i
$886$	−616.923	+	753.862i	−0.696302	+	0.850860i
$887$	−849.326	−	490.359i	−0.957526	−	0.552828i	−0.0621155	−	0.998069i	$-0.519785\pi$
$887$	−849.326	−	490.359i	−0.957526	−	0.552828i	−0.895411	+	0.445241i	$0.853118\pi$
$888$	−748.382	+	1414.31i	−0.842772	+	1.59269i
$889$		0			0
$890$	127.748	−	48.2844i	0.143538	−	0.0542521i
$891$	−219.449	+	380.096i	−0.246295	+	0.426595i
$892$	−13.4955	+	40.1232i	−0.0151294	+	0.0449812i
$893$	−778.228	+	449.310i	−0.871476	+	0.503147i
$894$	212.105	−	1295.93i	0.237254	−	1.44959i
$895$			88.6605i			0.0990621i
$896$		0			0
$897$	186.392			0.207795
$898$	−521.143	−	85.2956i	−0.580338	−	0.0949839i
$899$	−524.382	−	908.256i	−0.583295	−	1.01030i
$900$	227.627	+	76.5625i	0.252919	+	0.0850694i
$901$	−2003.98	−	1157.00i	−2.22417	−	1.28412i
$902$	−85.5391	−	226.315i	−0.0948327	−	0.250904i
$903$		0			0
$904$	97.4012	+	51.5398i	0.107745	+	0.0570131i
$905$	252.789	−	437.843i	0.279325	−	0.483805i
$906$	−606.410	−	496.256i	−0.669326	−	0.547743i
$907$	329.186	+	570.167i	0.362939	+	0.628629i	0.988443	−	0.151592i	$-0.0484399\pi$
$907$	329.186	+	570.167i	0.362939	+	0.628629i	−0.625504	+	0.780221i	$0.715107\pi$
$908$	83.7231	+	414.861i	0.0922061	+	0.456895i
$909$			52.1173i			0.0573348i
$910$		0			0
$911$		−	276.507i		−	0.303520i	−0.988417	−	0.151760i	$-0.951506\pi$
$911$		−	276.507i		−	0.303520i	0.988417	−	0.151760i	$-0.0484941\pi$
$912$	−1082.43	−	821.037i	−1.18688	−	0.900260i
$913$	−8.10765	−	14.0429i	−0.00888023	−	0.0153810i
$914$	−651.458	+	796.062i	−0.712755	+	0.870965i
$915$	99.6985	−	172.683i	0.108960	−	0.188724i
$916$	−198.111	−	224.636i	−0.216278	−	0.245236i
$917$		0			0
$918$	−362.274	−	958.487i	−0.394634	−	1.04410i
$919$	1160.24	+	669.867i	1.26251	+	0.728908i	0.973559	−	0.228437i	$-0.0733613\pi$
$919$	1160.24	+	669.867i	1.26251	+	0.728908i	0.288948	+	0.957345i	$0.406695\pi$
$920$	16.1138	+	436.446i	0.0175150	+	0.474398i
$921$	−381.250	−	660.344i	−0.413952	−	0.716986i
$922$	−65.3269	+	399.138i	−0.0708534	+	0.432904i
$923$	−158.392			−0.171606
$924$		0			0
$925$			1323.85i			1.43119i
$926$	233.447	−	1426.33i	0.252103	−	1.54031i
$927$	99.1324	−	57.2341i	0.106939	−	0.0617412i
$928$	520.900	−	494.731i	0.561315	−	0.533116i
$929$	17.7006	−	30.6583i	0.0190534	−	0.0330014i	−0.856342	−	0.516410i	$-0.827268\pi$
$929$	17.7006	−	30.6583i	0.0190534	−	0.0330014i	0.875395	+	0.483409i	$0.160601\pi$
$930$	−174.794	−	462.461i	−0.187950	−	0.497270i
$931$		0			0
$932$	1257.41	−	1108.93i	1.34915	−	1.18984i
$933$	36.6606	+	21.1660i	0.0392933	+	0.0226860i
$934$	439.879	−	537.519i	0.470962	−	0.575502i
$935$	142.418	−	82.2252i	0.152319	−	0.0879414i
$936$	−17.5122	−	27.9012i	−0.0187096	−	0.0298090i
$937$	−610.235			−0.651265			−0.325633	−	0.945496i	$-0.605577\pi$
$937$	−610.235			−0.651265			−0.325633	+	0.945496i	$0.605577\pi$
$938$		0			0
$939$	1399.99			1.49094
$940$	−44.3121	−	219.573i	−0.0471406	−	0.233589i
$941$	1604.66	−	926.450i	1.70527	−	0.984537i	0.765047	−	0.643975i	$-0.222716\pi$
$941$	1604.66	−	926.450i	1.70527	−	0.984537i	0.940222	−	0.340563i	$-0.110618\pi$
$942$	1121.08	+	917.438i	1.19011	+	0.973925i
$943$	822.752	+	475.016i	0.872483	+	0.503728i
$944$	−123.113	+	977.177i	−0.130416	+	1.03514i
$945$		0			0
$946$	54.4609	+	144.090i	0.0575697	+	0.152315i
$947$	916.448	−	1587.33i	0.967738	−	1.67617i	0.265666	−	0.964065i	$-0.414408\pi$
$947$	916.448	−	1587.33i	0.967738	−	1.67617i	0.702072	−	0.712106i	$-0.252259\pi$
$948$	−168.495	+	500.950i	−0.177737	+	0.528428i
$949$	93.0332	−	53.7128i	0.0980329	−	0.0565993i
$950$	−1109.27	−	181.554i	−1.16765	−	0.191109i
$951$			444.927i			0.467852i
$952$		0			0
$953$	349.687			0.366933			0.183467	−	0.983026i	$-0.441268\pi$
$953$	349.687			0.366933			0.183467	+	0.983026i	$0.441268\pi$
$954$	−83.9521	+	512.935i	−0.0880001	+	0.537668i
$955$	−75.2162	−	130.278i	−0.0787604	−	0.136417i
$956$	−189.135	+	562.316i	−0.197840	+	0.588196i
$957$	−297.733	−	171.896i	−0.311110	−	0.179620i
$958$	−54.5929	+	20.6342i	−0.0569864	+	0.0215388i
$959$		0			0
$960$	280.000	−	190.494i	0.291667	−	0.198431i
$961$	610.676	−	1057.72i	0.635459	−	1.10065i
$962$	115.002	−	140.530i	0.119545	−	0.146081i
$963$	−20.7208	−	35.8894i	−0.0215169	−	0.0372684i
$964$	−363.891	−	1803.14i	−0.377481	−	1.87047i
$965$			243.796i			0.252639i
$966$		0			0
$967$		−	632.128i		−	0.653700i	−0.945076	−	0.326850i	$-0.894013\pi$
$967$		−	632.128i		−	0.653700i	0.945076	−	0.326850i	$-0.105987\pi$
$968$	−683.568	+	429.042i	−0.706166	+	0.443225i
$969$	−1004.37	−	1739.62i	−1.03650	−	1.79528i
$970$	−230.546	−	188.667i	−0.237676	−	0.194502i
$971$	328.248	−	568.543i	0.338052	−	0.585523i	−0.646014	−	0.763325i	$-0.723565\pi$
$971$	328.248	−	568.543i	0.338052	−	0.585523i	0.984066	+	0.177802i	$0.0568988\pi$
$972$	−417.536	+	368.232i	−0.429564	+	0.378840i
$973$		0			0
$974$	1312.65	−	496.136i	1.34769	−	0.509380i
$975$	−103.557	−	59.7886i	−0.106212	−	0.0613217i
$976$	233.827	+	555.731i	0.239577	+	0.569397i
$977$	−84.6569	−	146.630i	−0.0866498	−	0.150082i	0.819443	−	0.573160i	$-0.194283\pi$
$977$	−84.6569	−	146.630i	−0.0866498	−	0.150082i	−0.906093	+	0.423078i	$0.860949\pi$
$978$	−1620.90	−	265.293i	−1.65736	−	0.271261i
$979$	197.616			0.201855
$980$		0			0
$981$		−	10.2337i		−	0.0104319i
$982$	118.328	+	19.3668i	0.120497	+	0.0197218i
$983$	−605.012	+	349.304i	−0.615475	+	0.355345i	−0.775105	−	0.631832i	$-0.782303\pi$
$983$	−605.012	+	349.304i	−0.615475	+	0.355345i	0.159630	+	0.987177i	$0.448970\pi$
$984$	−27.1796	−	736.165i	−0.0276216	−	0.748135i
$985$	96.1808	−	166.590i	0.0976455	−	0.169127i
$986$	993.588	−	375.541i	1.00770	−	0.380873i
$987$		0			0
$988$	101.980	+	115.634i	0.103218	+	0.117039i
$989$	−523.828	−	302.432i	−0.529654	−	0.305796i
$990$	−28.5862	−	23.3936i	−0.0288750	−	0.0236298i
$991$	372.133	−	214.851i	0.375513	−	0.216802i	−0.300352	−	0.953829i	$-0.597104\pi$
$991$	372.133	−	214.851i	0.375513	−	0.216802i	0.675864	+	0.737026i	$0.263771\pi$
$992$	1433.52	+	423.973i	1.44508	+	0.427392i
$993$	−731.529			−0.736686
$994$		0			0
$995$	−280.483			−0.281892
$996$	−9.76698	−	48.3969i	−0.00980621	−	0.0485912i
$997$	45.3720	−	26.1955i	0.0455085	−	0.0262743i	−0.477073	−	0.878864i	$-0.658302\pi$
$997$	45.3720	−	26.1955i	0.0455085	−	0.0262743i	0.522582	+	0.852589i	$0.324969\pi$
$998$	−106.757	+	130.454i	−0.106971	+	0.130716i
$999$	−1098.74	−	634.357i	−1.09984	−	0.634992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.j.275.1		8
7.2	even	3		392.3.g.h.99.4		4
7.3	odd	6		392.3.k.i.67.3		8
7.4	even	3	inner	392.3.k.j.67.3		8
7.5	odd	6		56.3.g.a.43.4	yes	4
7.6	odd	2		392.3.k.i.275.1		8
8.3	odd	2	inner	392.3.k.j.275.3		8
21.5	even	6		504.3.g.a.379.1		4
28.19	even	6		224.3.g.a.15.1		4
28.23	odd	6		1568.3.g.h.687.4		4
56.3	even	6		392.3.k.i.67.1		8
56.5	odd	6		224.3.g.a.15.2		4
56.11	odd	6	inner	392.3.k.j.67.1		8
56.19	even	6		56.3.g.a.43.3	✓	4
56.27	even	2		392.3.k.i.275.3		8
56.37	even	6		1568.3.g.h.687.3		4
56.51	odd	6		392.3.g.h.99.3		4
84.47	odd	6		2016.3.g.a.1135.3		4
112.5	odd	12		1792.3.d.g.1023.2		8
112.19	even	12		1792.3.d.g.1023.1		8
112.61	odd	12		1792.3.d.g.1023.7		8
112.75	even	12		1792.3.d.g.1023.8		8
168.5	even	6		2016.3.g.a.1135.2		4
168.131	odd	6		504.3.g.a.379.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.3	✓	4	56.19	even	6
56.3.g.a.43.4	yes	4	7.5	odd	6
224.3.g.a.15.1		4	28.19	even	6
224.3.g.a.15.2		4	56.5	odd	6
392.3.g.h.99.3		4	56.51	odd	6
392.3.g.h.99.4		4	7.2	even	3
392.3.k.i.67.1		8	56.3	even	6
392.3.k.i.67.3		8	7.3	odd	6
392.3.k.i.275.1		8	7.6	odd	2
392.3.k.i.275.3		8	56.27	even	2
392.3.k.j.67.1		8	56.11	odd	6	inner
392.3.k.j.67.3		8	7.4	even	3	inner
392.3.k.j.275.1		8	1.1	even	1	trivial
392.3.k.j.275.3		8	8.3	odd	2	inner
504.3.g.a.379.1		4	21.5	even	6
504.3.g.a.379.2		4	168.131	odd	6
1568.3.g.h.687.3		4	56.37	even	6
1568.3.g.h.687.4		4	28.23	odd	6
1792.3.d.g.1023.1		8	112.19	even	12
1792.3.d.g.1023.2		8	112.5	odd	12
1792.3.d.g.1023.7		8	112.61	odd	12
1792.3.d.g.1023.8		8	112.75	even	12
2016.3.g.a.1135.2		4	168.5	even	6
2016.3.g.a.1135.3		4	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +O(q^{10})\)	\(q+(-1.97374 - 0.323042i) q^{2} +(1.70711 + 2.95680i) q^{3} +(3.79129 + 1.27520i) q^{4} +(-1.34221 - 0.774923i) q^{5} +(-2.41421 - 6.38741i) q^{6} +(-7.07107 - 3.74166i) q^{8} +(-1.32843 + 2.30090i) q^{9} +(2.39883 + 1.96308i) q^{10} +(2.24264 + 3.88437i) q^{11} +(2.70163 + 13.3870i) q^{12} -1.54985i q^{13} -5.29150i q^{15} +(12.7477 + 9.66930i) q^{16} +(11.8284 + 20.4874i) q^{17} +(3.36526 - 4.11224i) q^{18} +(-12.4350 + 21.5381i) q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +(30.5055 + 17.6124i) q^{23} +(-1.00775 - 27.2951i) q^{24} +(-11.2990 - 19.5704i) q^{25} +(-0.500665 + 3.05899i) q^{26} +21.6569 q^{27} +22.4499i q^{29} +(-1.70938 + 10.4440i) q^{30} +(-40.4569 + 23.3578i) q^{31} +(-22.0371 - 23.2027i) q^{32} +(-7.65685 + 13.2621i) q^{33} +(-16.7279 - 44.2579i) q^{34} +(-7.97056 + 7.02938i) q^{36} +(-50.7340 - 29.2913i) q^{37} +(31.5012 - 38.4935i) q^{38} +(4.58258 - 2.64575i) q^{39} +(6.59133 + 10.5016i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(3.54915 + 17.5866i) q^{44} +(3.56604 - 2.05886i) q^{45} +(-54.5204 - 44.6168i) q^{46} +(31.2918 + 18.0663i) q^{47} +(-6.82843 + 54.1990i) q^{48} +(15.9792 + 42.2769i) q^{50} +(-40.3848 + 69.9485i) q^{51} +(1.97636 - 5.87591i) q^{52} +(-84.7102 + 48.9075i) q^{53} +(-42.7450 - 6.99607i) q^{54} -6.95149i q^{55} -84.9117 q^{57} +(7.25227 - 44.3103i) q^{58} +(30.7782 + 53.3094i) q^{59} +(6.74773 - 20.0616i) q^{60} +(32.6340 + 18.8412i) q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-1.20101 + 2.08021i) q^{65} +(19.3968 - 23.7024i) q^{66} +(16.6863 + 28.9015i) q^{67} +(18.7194 + 92.7574i) q^{68} +120.265i q^{69} -102.199i q^{71} +(18.0026 - 11.2993i) q^{72} +(34.6569 + 60.0274i) q^{73} +(90.6733 + 74.2026i) q^{74} +(38.5772 - 66.8176i) q^{75} +(-74.6102 + 65.8000i) q^{76} +(-9.89949 + 3.74166i) q^{78} +(33.5156 + 19.3503i) q^{79} +(-9.61710 - 22.8567i) q^{80} +(48.9264 + 84.7430i) q^{81} +(-53.2328 - 8.71262i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(33.8922 + 5.54714i) q^{86} +(-66.3799 + 38.3245i) q^{87} +(-1.32389 - 35.8578i) q^{88} +(22.0294 - 38.1561i) q^{89} +(-7.70354 + 2.91166i) q^{90} +(93.1960 + 105.674i) q^{92} +(-138.129 - 79.7486i) q^{93} +(-55.9256 - 45.7668i) q^{94} +(33.3807 - 19.2724i) q^{95} +(30.9861 - 104.769i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9	\( 8 q + 8 q^{3} + 12 q^{4} - 8 q^{6} + 12 q^{9} - 28 q^{10} - 16 q^{11} - 24 q^{12} - 8 q^{16} + 72 q^{17} - 16 q^{18} + 8 q^{19} - 112 q^{20} - 48 q^{22} - 40 q^{24} + 68 q^{25} + 28 q^{26} + 128 q^{27} - 16 q^{33} - 32 q^{34} + 72 q^{36} - 76 q^{38} + 56 q^{40} + 80 q^{41} - 160 q^{43} + 48 q^{44} - 224 q^{46} - 32 q^{48} + 224 q^{50} - 176 q^{51} - 56 q^{52} - 16 q^{54} - 272 q^{57} + 168 q^{58} + 184 q^{59} - 56 q^{60} + 224 q^{62} + 288 q^{64} - 168 q^{65} - 32 q^{66} + 224 q^{67} - 216 q^{68} + 160 q^{72} + 232 q^{73} + 280 q^{74} + 88 q^{75} + 48 q^{76} - 336 q^{80} + 52 q^{81} - 48 q^{82} - 176 q^{83} - 8 q^{86} - 240 q^{88} + 312 q^{89} - 616 q^{90} + 112 q^{92} - 112 q^{94} + 176 q^{96} + 272 q^{97} - 480 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 12 * q^4 - 8 * q^6 + 12 * q^9 - 28 * q^10 - 16 * q^11 - 24 * q^12 - 8 * q^16 + 72 * q^17 - 16 * q^18 + 8 * q^19 - 112 * q^20 - 48 * q^22 - 40 * q^24 + 68 * q^25 + 28 * q^26 + 128 * q^27 - 16 * q^33 - 32 * q^34 + 72 * q^36 - 76 * q^38 + 56 * q^40 + 80 * q^41 - 160 * q^43 + 48 * q^44 - 224 * q^46 - 32 * q^48 + 224 * q^50 - 176 * q^51 - 56 * q^52 - 16 * q^54 - 272 * q^57 + 168 * q^58 + 184 * q^59 - 56 * q^60 + 224 * q^62 + 288 * q^64 - 168 * q^65 - 32 * q^66 + 224 * q^67 - 216 * q^68 + 160 * q^72 + 232 * q^73 + 280 * q^74 + 88 * q^75 + 48 * q^76 - 336 * q^80 + 52 * q^81 - 48 * q^82 - 176 * q^83 - 8 * q^86 - 240 * q^88 + 312 * q^89 - 616 * q^90 + 112 * q^92 - 112 * q^94 + 176 * q^96 + 272 * q^97 - 480 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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